Chapter 08Basic sciencesLast reviewed: · What's new
Image Reconstruction and Processing
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Learning objectives and modules3 modules · about 2 h 25 min
Learning objectives
After this chapter you will be able to:
Explain projection, sinogram and filtered back projection; state the effect of the ramp filter.
Explain the principle of MLEM and OSEM and how the number of iterations and subsets affects contrast and noise.
Compare attenuation in SPECT and PET and the correction methods (Chang, CT-based).
Explain scatter correction methods (dual and triple energy window, model-based).
Explain the principle of ECG and respiratory gating and their place in motion correction.
Predict the effect of the filter cut-off frequency on resolution and noise; list acquisition modes and the basic requirements for quantitative analysis.
Modules
The chapter is divided into study modules without changing the order of the text: read, watch the animations, then answer the questions linked to those headings.
Photopeak window typically 10-20%; for 128 × 128 SPECT, 120 projections over 360° are sufficient
✓
Static / dynamic (1-5 s frames) / list mode (event-based, clinical in PET) / gated (ECG, respiratory)
✓
In PET, attenuation → depends on body size; in SPECT → depends on depth (Tc-99m brain: counts may fall by >4-fold)
✓
Partial volume → <2 × FWHM; more pronounced in SPECT; large ROI → total activity correct, mean concentration low
✓
Patlak → Ki (irreversible); Logan → VT (reversible); 2-compartment/4-constant → specific binding
✓
FBP: Analytical solution → fast → 1/r correction with ramp filter → noise-sensitive → streak artefacts → may produce negative values → limited modelling of physical factors → limited use today
✓
MLEM: Iterative → Poisson statistics → multiplicative update → no negative values → all projection data in every iteration → very slow → not suitable for clinical use
8.1 Filtered Back Projection (FBP)
8.1.1 Basic Concepts: Projection and Sinogram1 questions
In nuclear medicine imaging systems (SPECT and PET), cross-sectional (tomographic) images are created from projection data acquired from the patient at different angles. This process is called image reconstruction.
Projection data:
•
The gamma camera or PET detector views the patient from a given angle
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The 1D profile obtained at each angle forms a "projection"
•
A projection is the line integral of all activity at that angle
•
Mathematically it is defined by the Radon transform
Sinogram:
•
A 2D matrix formed by assembling the projection data acquired at all angles
•
X axis: Detector position (spatial location)
•
Y axis: Projection angle (0°-360° or 0°-180°)
•
Each row represents the projection profile at one angle
•
A point source forms a sinusoidal curve in the sinogram → hence the name "sinogram"
•
The sinogram is the input data of the reconstruction algorithm
BOARD TIP
▸
"How does a point source appear in the sinogram?"
→ As a sinusoidal curve. This is where the sinogram gets its name.
▸
"What does a straight vertical line in the sinogram mean?"
→ A fixed point source at the centre of rotation (projected at the same position at all angles).
Projections and sinogram of a phantom and images reconstructed with simple backprojection, filtered backprojection (FBP) and MLEM/OSEM, computed in the browser.
Continuous stream · no seeking
Key point: simple backprojection gives a star artefact and blurring; the ramp filter corrects this but raises noise; iterative methods fit the image step by step to the measured projections.
How to use: a single click on the images pauses and resumes; ↑ ↓ or the buttons above change that step's choice (object, number of projections, number of subsets); ← → change steps.
Speed
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Figure 8.1: Projection and sinogram: a point source at the centre forms a straight vertical line, an off-centre source forms a sinusoidal curve.
8.1.2 Simple Back Projection
Simple back projection is the most basic and intuitive reconstruction method:
Principle:
1. The projection data obtained at each angle are projected back into the image matrix along that angle (back projection)
2. The back-projected data from all angles are summed 3. When data from enough angles have been collected, an approximation of the activity distribution is obtained
Main problem – Star artefact (1/r blurring):
•
Simple back projection produces a blurred version of the true activity distribution
•
Around a point source, a star-shaped blur forms that falls off as 1/r (inversely proportional to distance)
•
This blur affects the whole image and causes loss of contrast
•
Mathematically: Simple back projection = true image ⊛ 1/r (convolution)
•
This problem is solved by filtering → Filtered Back Projection (FBP)
Projections and sinogram of a phantom and images reconstructed with simple backprojection, filtered backprojection (FBP) and MLEM/OSEM, computed in the browser.
Continuous stream · no seeking
Key point: simple backprojection gives a star artefact and blurring; the ramp filter corrects this but raises noise; iterative methods fit the image step by step to the measured projections.
How to use: a single click on the images pauses and resumes; ↑ ↓ or the buttons above change that step's choice (object, number of projections, number of subsets); ← → change steps.
Speed
Did this animation help you understand the topic?
Figure 8.2: In simple back projection, as the number of angles increases the star artefact turns into 1/r blurring; ramp-filtered FBP corrects this blurring.
The 1D Fourier transform of a projection profile equals a line through the 2D Fourier space (frequency space) of the image at that angle
•
This theorem shows that the frequency-space representation of the image can be obtained from projection data
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The Fourier data from all angles are combined and the image is formed by the inverse Fourier transform
Ramp filter:
•
A filter that increases in direct proportion to frequency in frequency space: H(f) = |f|
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Suppresses low frequencies, amplifies high frequencies
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Corrects 1/r blurring exactly in mathematical terms
•
Problem: Because it amplifies high frequencies, it also increases noise
•
For this reason the ramp filter is not used alone in practice → it is used together with a window function
Steps of the FBP algorithm:
1. Projection data are acquired at each angle 2. A 1D Fourier transform is applied to each projection profile 3. The ramp filter (+ window function) is applied in frequency space 4. The filtered projection is obtained by the inverse Fourier transform 5. The filtered projections are back-projected 6. The back-projected data from all angles are summed to form the cross-sectional image
Figure 8.3: Fourier slice theorem and the steps of the FBP algorithm (schematic).
Did this figure help you understand the topic?
Advantages of FBP:
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High computation speed (analytical solution)
•
Mathematically well defined
•
Reproducible results (operator-independent)
•
Historically the standard method
Disadvantages of FBP:
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Sensitive to noise (especially in low-count studies)
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Streak artefacts (linear artefacts) may occur
•
Limited capacity to model physical factors (attenuation, scatter, detector response)
•
May produce negative values (physically meaningless)
•
Severe artefacts with incomplete data (limited angle, truncation)
BOARD TIP
▸
"What is the function of the ramp filter in FBP?"
→ To correct 1/r blurring.
▸
"Disadvantage of the ramp filter?"
→ It amplifies high frequencies → noise increases.
▸
"The most important disadvantage of FBP?"
→ Sensitivity to noise and inability to model physical factors.
▸
"Can negative values occur in FBP?"
→ YES → physically meaningless.
8.2 Iterative Reconstruction (OSEM, MLEM)
8.2.1 Basic Principle of Iterative Reconstruction2 questions
Iterative reconstruction is a method that approaches the true activity distribution by improving the image step by step (iteration). Unlike FBP, it uses a cycle of successive estimation and correction instead of an analytical solution.
General algorithm:
1. Initial estimate: Start with a uniform image 2. Forward projection: Simulated projection data are calculated from the estimated image
–
In this step, physical factors (attenuation, scatter, detector response, PSF) can be included in the model → system matrix
3. Comparison: The calculated projection data are compared with the true (measured) projection data
4. Update: The image estimate is updated using the difference or the ratio 5. Repeat: Steps 2-4 are repeated until a convergence criterion is met or a set number of iterations is reached
Advantages of iterative reconstruction (compared with FBP):
•
Can include physical factors (attenuation, scatter, detector response/PSF, partial volume) in the model
•
Better image quality in low-count studies
•
Does not produce negative values (in ML-based algorithms)
•
Better noise control
•
More robust with incomplete data
•
No streak artefacts
Disadvantages of iterative reconstruction:
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Longer computation time (but no longer a problem with modern computers)
•
Dependent on parameter choice (number of iterations, number of subsets)
•
Excessive iterations → noise amplification
•
Gibbs artefact (ring-shaped artefact at the edges of hot spots)
•
Convergence speed and quality may depend on the initial estimate
Projections and sinogram of a phantom and images reconstructed with simple backprojection, filtered backprojection (FBP) and MLEM/OSEM, computed in the browser.
Continuous stream · no seeking
Key point: simple backprojection gives a star artefact and blurring; the ramp filter corrects this but raises noise; iterative methods fit the image step by step to the measured projections.
How to use: a single click on the images pauses and resumes; ↑ ↓ or the buttons above change that step's choice (object, number of projections, number of subsets); ← → change steps.
Speed
Did this animation help you understand the topic?
Figure 8.4: The iterative reconstruction loop and, in OSEM, division of the projections into equally spaced subsets (schematic).
Effective number of iterations:
Effective iterations = Number of iterations × Number of subsets
Choosing OSEM parameters:
•
Iterations↑: Resolution↑, contrast↑ → but noise↑
•
Iterations↓: Noise↓ → but resolution↓, contrast↓, blurring↑
•
Subsets↑: Acceleration↑ → but with too many subsets convergence may become unstable
•
Optimal parameter choice: Balance between resolution and noise → depends on the clinical task
BOARD TIP
▸
"The standard reconstruction algorithm in SPECT and PET today?"
→ OSEM.
▸
"How much faster is OSEM than MLEM?"
→ ~As many times as the number of subsets.
▸
"2 iterations × 10 subsets equal how many MLEM-equivalent updates?"
→ 20.
▸
"What happens if the number of iterations is increased?"
→ Resolution and contrast increase BUT noise also increases.
In modern iterative reconstruction algorithms, the point spread function (PSF) of the detector can be included in the system matrix.
Effects of PSF modelling:
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Spatial resolution improves (especially away from the centre)
•
Partial volume effect decreases → detection of small lesions improves
•
SUV values may increase (in PET)
•
Gibbs artefact (Gibbs ringing): Ring-shaped excessively high values at the edges of hot spots → spuriously increased uptake
Figure 8.5: As the number of iterations increases, contrast and noise increase together; PSF modelling sharpens edges but may create Gibbs overshoot (simulation).
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Commercial names:
•
Siemens: HD·PET, xSPECT
•
GE: Evolution (SPECT), SharpIR (PET; VUE Point FX = TOF)
•
Philips: Astonish (SPECT)
BOARD TIP
▸
"The most important artefact of PSF modelling?"
→ Gibbs artefact (Gibbs ringing) → ring-shaped spuriously increased uptake at the edges of hot spots.
▸
"How does PSF modelling affect SUV?"
→ SUV may increase (owing to partial volume correction) → consistent reconstruction parameters must be used in follow-up studies.
8.2.5 FBP vs Iterative Reconstruction
Feature
FBP
Iterative (OSEM)
Computation speed
Very fast
Slower (but acceptable on modern systems)
Noise control
Poor
Good
Modelling of physical factors
Limited
Comprehensive (attenuation, scatter, PSF)
Low-count studies
Poor (streak artefact)
Good
Negative values
May occur
Do not occur (ML-based)
Quantitative accuracy
Low
High
Parameter dependence
Low
High (choice of iterations, subsets)
Use today
Limited (research)
Standard clinical use
8.3 Attenuation Correction (CT-Based, Chang)
8.3.1 The Attenuation Problem
Gamma photons emitted from the patient's body are absorbed or scattered by tissue before reaching the detector. This process is called attenuation and, if not corrected, causes serious quantitative errors and artefacts.
Effects of attenuation:
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Activity in deep structures appears lower than it is → spuriously decreased uptake
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Activity in superficial structures appears relatively high
•
Even in a phantom with a uniform activity distribution, a centre-to-periphery gradient forms
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Quantitative measurements (SUV, uptake) are calculated incorrectly
Attenuation coefficient:
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Linear attenuation coefficient of soft tissue at 140 keV (Tc-99m): µ ≈ 0.15 cm⁻¹
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Linear attenuation coefficient of soft tissue at 511 keV (PET): µ ≈ 0.096 cm⁻¹
•
Although attenuation appears lower in PET, the total attenuation is high when the photon pair (two photons) is considered together
•
Attenuation correction is mandatory in PET (photon pair attenuation)
•
Attenuation correction is recommended in SPECT, but uncorrected images can also be evaluated
In an axial body section, photons from a source are attenuated in tissue. In SPECT the fraction of single photons reaching the camera falls with source depth; in PET the chance that both photons escape does not depend on depth, only on total thickness. The last step compares uncorrected and Chang- or CT-corrected images and profiles of a uniform phantom.
Continuous stream · no seeking
Key point: in SPECT attenuation depends on source depth (deep structures look faint); in PET the attenuation of the photon pair depends only on total thickness, so a transmission (CT) measurement corrects it exactly and correction is mandatory.
Source: book (soft-tissue µ ≈ 0.15 cm⁻¹ at 140 keV and ≈ 0.096 at 511 keV; deep structures low, centre-to-periphery gradient; pair attenuation in PET depends on total thickness; Chang and CT-based correction); NIST XCOM water 0.154 / 0.0960 cm⁻¹. Interaction points are sampled from an exponential distribution. Phantom: 20 cm uniform disc, 64 × 64 (4 mm), 128 angles, ramp-filtered FBP, first-order Chang. Patient thickness 20 cm illustrative; scattered photons that are still detected are not shown. Atomic scale: interaction fractions in water from NIST XCOM (140.5 keV: Compton 97.6%, coherent 1.8%, photoelectric 0.6%; 511 keV: Compton 99.8%); angles from the Klein–Nishina distribution; the 435–650 keV PET window is a typical LSO/LYSO setting. The atom is not drawn to scale.
How to use: a single click on the drawing pauses and resumes; ↑ ↓ or the buttons below change the source depth; ← → change steps.
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Figure 8.6: In SPECT, attenuation depends on source depth; in PET, attenuation of the photon pair depends only on the total thickness (D).
BOARD TIP
▸
"Soft tissue µ for Tc-99m (140 keV)?"
→ ~0.15 cm⁻¹.
▸
"Soft tissue µ for 511 keV?"
→ ~0.096 cm⁻¹.
▸
"Is attenuation correction mandatory in PET?"
→ YES → photon pair attenuation is very high.
▸
"Is attenuation correction mandatory in SPECT?"
→ Not mandatory but recommended (especially in cardiac SPECT).
In PET, two photons (511 keV) are attenuated together. The total attenuation depends on the path length of the photon pair through the whole thickness of the patient and is independent of the source position.
ACF = e+µ·D (attenuation factor = e−µ·D)
Here D is the total path length travelled by the photon pair (patient thickness). This property is specific to PET and simplifies attenuation correction.
PET attenuation correction methods:
1. Transmission source (old method):
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Ge-68/Ga-68 or Cs-137 rod source
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Transmission scans are acquired with and without the patient (blank scan)
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The attenuation map is created by taking the ratio
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Disadvantages: Long scan time, noisy map, additional radiation source
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No longer used today (replaced by PET/CT)
2. CT-based attenuation correction (CTAC) – Standard method:
"Why is attenuation correction in PET different from SPECT?"
→ In PET the photon pair is attenuated together → total attenuation is independent of source position and depends only on patient thickness.
▸
"The old attenuation correction method in PET?"
→ Transmission source (Ge-68 or Cs-137).
▸
"The standard today?"
→ CTAC.
8.4 Scatter Correction
8.4.1 The Scatter Problem
Compton scattering causes a photon to reach the detector after changing its direction and energy. Scattered photons are recorded at the wrong location → loss of image contrast and quantitative error.
In nuclear medicine imaging, motion is an important problem that seriously affects image quality and quantitative accuracy.
Types of motion:
1. Physiological motion:
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Respiratory motion: The most important source of motion. The diaphragm moves 1-2 cm vertically. The lung bases and liver dome are the most affected regions. In cardiac imaging it may cause inferior wall artefacts.
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Cardiac motion: Contraction and relaxation of the myocardium during the cardiac cycle. Affects assessment of wall thickness and motion in cardiac SPECT and PET.
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Peristaltic motion: Bowel movements in GI studies
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Bladder filling: Activity changing over time in pelvic studies
2. Voluntary/involuntary patient motion:
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Change of position, coughing, sneezing
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More pronounced with long acquisition times
–
More frequent in children and agitated patients
Effects of motion on the image:
•
Blurring → loss of spatial resolution
•
SUV measured lower than it is (increased partial volume effect)
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Lesion size appearing larger than it is
•
Emission–CT misregistration in PET/CT and SPECT/CT → attenuation correction errors
Gating is a technique that reduces motion artefacts by "freezing" physiological motion. Physiological signals (ECG, respiration) are recorded during acquisition and the data are sorted according to motion phases.
1. Cardiac Gating (ECG Gating):
Principle:
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The R-R interval is determined from the ECG signal
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Each R-R interval is divided into equal time slices (frames/bins) → typically 8 or 16 frames
•
Each frame represents a particular phase of the cardiac cycle
•
Result: A separate image set for each phase → cine loop
Gated PET: The same parameters + higher resolution
•
MUGA (radionuclide ventriculography): LVEF, RVEF, wall motion, phase analysis
LVEF calculation (gated SPECT/PET):
LVEF = (EDV − ESV) / EDV × 100
•
EDV: End-diastolic volume (largest volume → usually frame 1)
•
ESV: End-systolic volume (smallest volume → usually frame 3-4/8 or 6-8/16)
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Automatic contour detection algorithms are used (QGS, Emory Cardiac Toolbox, etc.)
Gating problems:
•
Irregular R-R interval in patients with arrhythmia → beat rejection is needed
•
Acceptance window: Beats outside ±20% of the mean R-R interval are rejected
•
Excessive beat rejection → loss of counts → noisy images
•
In tachycardia, short R-R → frame duration shortens → temporal sampling becomes difficult
•
Arrhythmia → rejected beats → loss of counts and gating artefact
BOARD TIP
▸
"Typical number of frames in gated SPECT?"
→ 8 or 16.
▸
"LVEF formula?"
→ (EDV-ESV)/EDV × 100.
▸
"Gating problem in a patient with arrhythmia?"
→ Irregular R-R → beat rejection is needed → beats outside the acceptance window are rejected.
▸
"Gating quality in tachycardia?"
→ Low (short R-R → few counts per frame → noise).
2. Respiratory Gating:
Principle:
•
The respiratory signal is recorded (chest wall sensor, bellows, RPM system, CT-based)
•
The respiratory cycle is divided into phases (typically 4-10 phases)
•
A separate image is formed for each phase
•
The end-expiration phase is the most stable phase → this phase is usually evaluated
Respiratory gating methods:
•
Phase-based: The respiratory cycle is divided into equal phases → problematic with irregular breathing
•
Amplitude-based: Divided according to respiratory amplitude → better with irregular breathing
•
Duty cycle: Ratio of the respiratory phase used to the total acquisition time → low duty cycle = few counts = noise
In the ECG strip each R-R interval is divided into frames, a short-axis section of the left ventricle beats, and LVEF is calculated from the frame-averaged volume curve. The second step rejects beats outside the mean R-R ±20% in a variable rhythm and shows the R-R distribution. The third step bins an irregular breathing signal by phase or amplitude and compares the diaphragm range and time share of each bin.
Continuous stream · no seeking
Key point: gating freezes motion by sorting counts by cardiac or respiratory phase; with irregular R-R, beat rejection costs counts, and with phase-based respiratory binning irregular breaths blur the image; end-expiration is the most stable phase.
Source: book (R-R in 8 or 16 frames; LVEF = (EDV − ESV)/EDV; EDV usually frame 1, ESV 3-4 of 8; acceptance window mean R-R ±20%; breathing 4-10 phases, phase- and amplitude-based, end-expiration most stable, duty cycle). Volume curve illustrative (EDV 120, ESV 50 mL, minimum at 37% of R-R); myocardial volume kept constant in the short-axis ring. R-R sequences illustrative (PVC 620/1380 ms; AF 500-1150 ms). Breathing: Lujan 1999 model d = A·cos⁴(πt/τ), τ = 4 s, amplitudes 1.4-3.0 cm illustrative.
How to use: a single click on the drawing pauses and resumes; the buttons below the drawing pick the number of frames, the rhythm and the method; ← → change steps and selections.
Speed
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Figure 8.8: ECG gating (8 frames, rejection of a short R-R beat, volume curve) and phase-based and amplitude-based binning in respiratory gating (schematic).
Clinical applications:
•
Assessment of lung nodules on PET/CT (reducing respiratory artefact)
•
Correction of diaphragmatic motion in cardiac PET
•
Improving SUV accuracy in liver dome lesions
•
Radiotherapy planning (4D-PET/CT)
3. Dual Gating (Cardiac + Respiratory):
–
Both ECG and respiratory signals are recorded simultaneously
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A separate image for each cardiac phase × each respiratory phase → many bins
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Best motion correction but very few counts per frame → noise problem
Elastic registration between respiratory gating phases → all phases are combined into a single image
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Provides motion correction without loss of counts
–
Computationally intensive but feasible on modern systems
3. Data-driven motion correction:
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Motion information is extracted from the PET/SPECT data themselves, without an external sensor
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A respiratory signal is derived from list-mode data
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Removes the need for an external sensor
BOARD TIP
▸
"The most stable phase in respiratory gating?"
→ End-expiration.
▸
"Why is dual gating limited in clinical practice?"
→ Too many bins → very few counts per frame → noise.
▸
"Which motion correction method is suitable for brain imaging?"
→ Rigid body registration (the brain is a rigid structure).
8.6 Filters and Image Processing Parameters
8.6.1 Frequency Space and the Fourier Transform
In image processing, filters are usually defined in frequency space. The Fourier transform converts an image from the spatial domain to the frequency domain.
Basic concepts:
•
Low frequencies: General structure of the image, large structures, contrast → signal
•
High frequencies: Fine detail, edges → but also noise
•
Nyquist frequency: The highest frequency that can be sampled = 1 / (2 × pixel size)
Filters used in nuclear medicine fall into two main categories:
1. Smoothing (Low-pass) Filters:
Suppress high frequencies → noise decreases but resolution falls.
a) Butterworth filter:
H(f) = 1 / √(1 + (f/fc)2n)
•
fc: Cutoff frequency → the point at which amplitude falls to ~70.7% (−3 dB)
•
n: Filter order → determines the sharpness of the transition
•
Cutoff frequency↑: Less smoothing → resolution↑, noise↑
•
Cutoff frequency↓: More smoothing → noise↓, resolution↓
•
Order↑: Sharper transition → approaches the ideal low-pass but with risk of ringing artefact
•
The most widely used filter in nuclear medicine
•
Typical parameters: Cutoff frequency 0.3-0.5 Nyquist, order 5-10
b) Gaussian filter:
H(f) = e−2π²σ²f²
•
σ: Standard deviation → FWHM = 2.355 × σ
•
FWHM↑: More smoothing → noise↓, resolution↓
•
Does not create ringing artefact (smooth transition)
•
Widely used in PET for post-reconstruction smoothing
•
Typical FWHM: 4-8 mm (PET), 8-15 mm (SPECT)
c) Hanning (Hann) filter:
H(f) = 0.5 + 0.5 cos(π f / fc), f ≤ fc
•
Zero above the cutoff frequency → complete cutoff
•
Used in FBP as a window function together with the ramp filter
•
More aggressive smoothing than Butterworth
d) Hamming filter:
H(f) = 0.54 + 0.46 cos(π f / fc), f ≤ fc
•
Similar to Hanning but does not fall exactly to zero at the cutoff frequency (minimum value 0.08)
•
Slightly less smoothing than Hanning
2. Sharpening (High-pass) Filters:
–
Amplify high frequencies → edges become sharper but noise increases
–
Rarely used alone in nuclear medicine
–
Metz and Wiener filters: Both smoothing and sharpening properties → attempt to correct the detector response
3. Ramp filter:
–
Specific to FBP → corrects 1/r blurring
–
H(f) = |f| → directly proportional to frequency
–
Not used alone → together with a window function (Hanning, Hamming, Butterworth)
–
At the same cutoff frequency, the smoothing strength of window functions increases in this order: Ramp (no smoothing) < Shepp-Logan < Hamming < Hanning < Parzen. Parzen gives the smoothest and least noisy image, but also the lowest resolution
Figure 8.9: Effect of cutoff frequency and order in the Butterworth filter; combination of the ramp filter with a window function in FBP.
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BOARD TIP
▸
"The most widely used filter in nuclear medicine?"
→ Butterworth.
▸
"If the cutoff frequency of a Butterworth filter is increased?"
→ Less smoothing → resolution↑ BUT noise↑.
▸
"If the cutoff frequency is decreased?"
→ More smoothing → noise↓ BUT resolution↓.
▸
"If FWHM is increased in a Gaussian filter?"
→ More smoothing → noise↓, resolution↓.
▸
"Why is the ramp filter not used alone in FBP?"
→ It amplifies high frequencies → noise increases greatly → a window function is needed.
8.6.3 Filter Selection and Clinical Use
Filter selection is based on the balance between resolution and noise and depends on the clinical task:
Detection of small lesions → less smoothing (resolution takes priority)
•
Assessment of diffuse disease → more smoothing is acceptable
•
A smoothing filter can be applied before reconstruction to the 2D projections (prefiltering; in FBP together with the ramp filter) or after reconstruction to the 3D volume (postfiltering)
Clinical examples:
•
Bone SPECT: High counts → Butterworth cutoff frequency 0.4-0.5 Nyquist
•
Cardiac SPECT: Moderate counts → Butterworth cutoff frequency 0.3-0.4 Nyquist
•
PET: Gaussian FWHM 4-6 mm (when high resolution is wanted) or 6-8 mm (when low noise is wanted)
Large matrix → small pixel → better spatial sampling → but fewer counts per pixel → noise↑
•
Pixel depth: In byte (8-bit) mode a pixel can hold at most 255 counts, in word (16-bit) mode 65,535. The memory requirement increases with the square of the matrix side (a 64 × 64 image takes up 1/16 of the space of a 256 × 256 image)
•
Pixel size = FOV / (matrix × zoom factor). Zoom makes the pixel smaller but also narrows the displayed field (e.g. with a 25 cm FOV and a 256 × 256 matrix the pixel is ~1 mm)
•
On screen, counts are displayed scaled to a grey or colour scale (LUT). A logarithmic scale emphasises differences in low-count regions and an exponential scale in high-count regions; windowing does not change the data
Pixel size and the sampling rule:
•
The pixel size should be 1/2 - 1/3 of the system's spatial resolution (FWHM) (Nyquist sampling criterion)
•
Example: SPECT resolution ~12 mm → pixel size ≤ 4-6 mm → 128 × 128 matrix (FOV 40 cm → pixel ~3.1 mm) or 64 × 64 with zoom
•
Example: PET resolution ~5 mm → pixel size ≤ 1.7-2.5 mm → 200 × 200 or larger matrix
Undersampling:
•
Pixel size too large → Nyquist criterion not met → aliasing artefact
•
Pixel size too small → unnecessary data → increased noise (counts/pixel fall)
8.6.5 Number of Projections and Angular Sampling3 questions
Number of projections in SPECT:
•
Typically 60-128 projections (over a 360° rotation)
•
Theoretical angular sampling rule (Nyquist): the number of projections needed for 180° data ≈ π/2 × the number of pixels across the object diameter. In practice, a number of projections over 360° close to the matrix size (60-64 for 64 × 64; 120-128 for 128 × 128) is considered sufficient
–
64 × 64 matrix: in practice 60-64 projections over 360° (6°-5.6° steps) are sufficient
–
128 × 128 matrix: in practice 120-128 projections over 360° (3°-2.8° steps) are sufficient; the recommended value is 120 projections
•
Too few projections → streak artefacts (especially pronounced in FBP)
•
Too many projections → unnecessarily long acquisition time
SPECT acquisition orbit:
•
Circular orbit: Simple, standard → but variable patient–detector distance → loss of resolution
•
Body contour orbit (body contouring / non-circular orbit): The detector rotates as close to the patient as possible → resolution improves → the preferred method
•
Step-and-shoot: Stops at each angle to acquire data → little motion artefact
•
Continuous rotation: Acquires data while rotating continuously → faster but with angular blurring
Gamma camera heads rotating around a thoracic cross-section: 180° opposed and L-mode configurations, the angles acquired, and system resolution on circular and body-contour orbits are shown.
Continuous stream · no seeking
Key point: two opposed heads collect 360° of data in a 180° rotation; in cardiac imaging L-mode covers only the anterior 180° near the heart; a body-contour orbit keeps the detector close to the patient and preserves resolution.
Source: book (dual head 180°/90°, cardiac RAO 45° → LPO 45°, 60–128 projections over 360° and 32–64 for cardiac, 15–40 s per projection). Example: 128 and 64 projections, 20 s per projection, rotation time excluded. Body section 36 × 24 cm (illustrative), collimator 1.5 cm from the body. Resolution with the LEHR values of the collimator animation: Rc = d·(L + z)/L, Rs = √(Ri² + Rc²) (d 1.5 mm, L 35 mm, Ri 3.5 mm). Drawing to scale; heads with 40 cm field of view.
How to use: a single click on the drawing pauses and resumes; in the orbit step ↑ ↓ switch between the circular and the body-contour orbit; ← → change steps.
Speed
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Figure 8.10: Circular and body contour SPECT orbits (schematic).
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Practical recommendation: With a 128 × 128 matrix, 120 projections over 360° (3° steps) are considered sufficient; the required angular sampling varies with the number of detectors, the arc and the matrix
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"The preferred orbit in SPECT?"
→ Body contour (body contouring) → detector close to the patient → resolution↑.
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"Consequence of too few projections?"
→ Streak artefacts.
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"How large should the pixel size be?"
→ 1/2 - 1/3 of the system FWHM (Nyquist criterion).
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"64 × 64 matrix or 128 × 128 matrix?"
→ If counts are sufficient, 128 × 128 gives better resolution but counts per pixel decrease.
A digital image is a matrix of numerical values that a computer can read and process
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The aim of acquisition systems is to optimise spatial resolution, detection efficiency (in terms of dead time) and energy resolution
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There are three types of acquisition in nuclear medicine: single photon (planar and SPECT), positron (PET) and imaging triggered by a physiological signal (gated)
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Key variables: Matrix size, acquisition time or stopping condition, system resolution, system sensitivity, dead time and energy resolution
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The acceptance window centred on the photopeak is usually 10-20% wide
Static acquisition:
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The image is acquired until a set time has elapsed or a preset total count is reached
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For single-FOV static images the matrix is usually between 128 × 128 and 2048 × 2048
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Whole-body scan with a gamma camera: Anterior and posterior images are acquired simultaneously with two opposed (180°) detectors; time ~20-45 min, output usually at most 256 × 1024 pixels
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SAFOV-PET scans the whole body either with overlapping bed positions (step-and-shoot) or with continuous bed motion
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Static protocols assume that the tracer has reached equilibrium and that the activity concentration does not change during acquisition
Dynamic acquisition:
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Recording of short (e.g. 1-5 s) consecutive frames at time intervals set by the operator → 2D + time data in planar imaging, 3D + time data in SPECT/PET
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A time–activity curve (TAC) and cine display are obtained; in TAC analysis, attention must be paid to background correction and partial volume spill-over from neighbouring regions
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Important for fully quantitative parametric PET and for characterising the pharmacokinetics of new radiopharmaceuticals; in routine clinical practice time and workload are limiting
List mode:
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Each event is recorded individually with its detected coordinates and time stamp; the data can later be divided into any desired time intervals or gates
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Used clinically in PET; in SPECT it is mostly available for research only
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Useful for dynamic PET and motion correction; in return, the data volume is large
Gated acquisition:
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Usually synchronised to the ECG, less often to respiration; the physiological cycle is divided into bins
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Main limitation: Few counts per gate and the resulting poor statistics
Digital Image Formats and Information Systems
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Interfile: a format used predominantly in nuclear medicine; its final version (version 3) was defined in 1992. Its metadata are in ASCII, so they can be read and edited with any text editor. It has largely been replaced by DICOM
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DICOM: grew out of the ACR-NEMA collaboration and took the name DICOM with version 3. It is not only a file format; it also defines a transmission protocol, query and retrieval, and workflow management
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The top level of organisation is the study: each study is linked to a single patient, and a patient may have many studies; the series and image levels follow. The basic unit was originally the 2D image; in the later multiframe format a volume, a time series, a gated sequence or data from different photopeaks can be held in one file. Nuclear medicine uses the multiframe format more than other modalities
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PACS: images are stored in a picture archiving and communication system (PACS) that is separate from, but coordinated with, the RIS; DICOM is the predominant standard for PACS
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RIS: supports scheduling, performing, reporting and billing; nuclear medicine studies that extend over several days may not be handled well by a general-purpose RIS. Selecting the patient from the RIS worklist leads to far fewer errors than re-entering the identifying data for each study
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HL7: a standard message format between hospital information systems. An information gateway (a 'broker' within a department) connects the systems; because each system connects only to the gateway, complexity grows roughly with n rather than n²
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Compression: lossless methods (run-length, LZW) reproduce the original image exactly and reduce its size by a factor of 2-3; lossy methods reduce it by a factor of 15-25, but the original image cannot be recovered exactly
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Tele-nuclear medicine (SNMMI/EANM 2.0, 2014): interpretation of, or consultation on, images at a remote station; distribution within a single institution is the domain of PACS
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All information needed for interpretation is available at the remote station: demographic and clinical data, indication, procedure details, other relevant tests, correlative CT and MR images, technical problems. Every image is explicitly associated with the patient identifier
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The remote station provides the same (or equivalent) display and processing functions as the on-site workstation: comparison display, adjustment of lower and upper levels, colour tables, cine display, fusion and three-plane display, ROI and SUVmax/SUVmean measurement. Smartphones and tablets facilitate consultation but have limited utility for interpretation and reporting
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The communication protocol should confirm reliable transmission; encryption improves security over public networks. If lossy compression is used, the remote data should be diagnostically comparable to the original; the adequacy of lossy compression for primary interpretation and the legal aspects of remote interpretation are not yet settled
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The remote monitor undergoes the same quality control as on-site monitors: the SMPTE test pattern checks resolution and linearity, and a grey-scale pattern checks discontinuities that create artificial edges. On a multi-use computer a change in colour depth (e.g. 256 colours) can impair interpretation and may not be obvious at first glance; systems that show a test pattern at login facilitate regular checks
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Security emphasises login control and access to databases containing patient information rather than encryption of pure image data; there is a time-out appropriate to the environment and a disaster recovery plan for a security breach or loss of data
8.7.2 Prerequisites and Error Sources of Quantitative Imaging4 questions
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The aim of quantitative nuclear medicine is to determine the absolute in vivo activity concentration (Bq/mL) within an ROI. For this, physical factors, device performance, protocol and patient-related factors must be corrected (for details, see the EANM guideline on quantitative SPECT/CT)
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Attenuation: Ax = A₀ × e−µd. It is a bigger problem in single-photon imaging than in PET (e.g. in brain imaging with Tc-99m the detected counts may fall by more than 4-fold)
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The effective atomic number of most body tissues is below 10; therefore Compton scattering dominates at the photon energies used in nuclear medicine
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In PET, attenuation depends on body size, not on the depth of emission; in SPECT, the quantitative error is more pronounced for deep-seated lesions
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Scatter: Because single-photon systems have better energy resolution, window-based correction is easier; in PET, modelling of coincidences that have undergone single Compton scattering is the standard approach
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Dead time: Comes to the fore especially in dynamic studies at moments of high activity such as the first bolus pass; it can be corrected if the count-rate characteristics of the system are known
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Partial volume effect: In objects smaller than ~2 times the system resolution, activity spreads outside the physical boundaries. It is more pronounced in single-photon imaging than in PET and can cause ROIs to be drawn larger than they are in automatic segmentation
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When the ROI is enlarged, total activity is recovered but mean concentration falls. Alternatively, recovery coefficients obtained from hot-sphere phantoms can be used (assuming a spherical lesion and a uniform background)
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Resolution modelling can be included in reconstruction; in SPECT, septal penetration and collimator scatter are also modelled
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Respiratory and cardiac motion can be monitored and gated with a pressure belt, spirometer, reflective markers and ECG. When CT is acquired during breath-hold while the emission image reflects the respiratory average, this causes quantitative error in attenuation correction
ROI/VOI definition and SUV:
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To obtain a quantitative or semi-quantitative parameter, the ROI/VOI must be defined manually, with a fixed threshold or with more advanced methods
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Fixed-threshold segmentation: All voxels exceeding a preset threshold are included in the VOI
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In PET, functional tumour volume and SUV have both predictive and prognostic value; radiomics quantifies heterogeneity in the activity distribution by histogram and texture analysis
8.7.3 Kinetic Modelling and Parametric Imaging4 questions
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Cumulated activity can also be calculated with the trapezoidal rule without building a pharmacokinetic model (by estimating the half-life of the final phase)
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In compartmental modelling, the organ is treated as if it consisted of homogeneous compartments; transfers between compartments are described by rate constants (K₁, k₂, k₃, k₄) and differential equations
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A one-tissue-compartment, two-constant (K₁, k₂) model mostly represents non-specific uptake; a two-tissue-compartment, four-constant (K₁-k₄) model represents a specific binding compartment
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Kinetics can be modelled as reversible (e.g. receptor ligands) or irreversible (e.g. FDG, k₄ ≈ 0)
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The blood input function is obtained by arterial sampling or from the image; alternatively a reference tissue can be used (reference tissue models)
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Parameters that can be calculated: Apparent volume of distribution (VT), blood clearance, binding potential (BPND) and receptor occupancy
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Graphical analysis: The Patlak plot gives the net influx constant (Ki) for irreversible uptake, and the Logan plot gives VT for reversible binding
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In parametric imaging the dynamic series is converted into a single image in which each voxel shows a physiological parameter (e.g. Ki); ROI-based TACs may become unnecessary
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Whole-body dynamic/parametric imaging can be performed with LAFOV PET or with multi-bed parametric protocols
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Population (non-linear mixed-effects) and Bayesian modelling allow kinetic estimation with fewer imaging sessions and are less affected by missing data
Figure 8.11: Two-tissue compartment model with Patlak and Logan graphical analyses (schematic).
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Patlak: irreversible uptake (FDG) → Ki. Logan: reversible binding → VT. One tissue compartment/two constants → non-specific uptake; two tissue compartments/four constants → specific binding. List mode is clinical in PET and mostly for research in SPECT. The partial volume effect is more pronounced in SPECT than in PET.
Key Points for the Board
Acquisition and Quantitative Analysis – Additional Points
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Photopeak window typically 10-20%; for 128 × 128 SPECT, 120 projections over 360° are sufficient
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Static / dynamic (1-5 s frames) / list mode (event-based, clinical in PET) / gated (ECG, respiratory)
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In PET, attenuation → depends on body size; in SPECT → depends on depth (Tc-99m brain: counts may fall by >4-fold)
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Partial volume → <2 × FWHM; more pronounced in SPECT; large ROI → total activity correct, mean concentration low
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Patlak → Ki (irreversible); Logan → VT (reversible); 2-compartment/4-constant → specific binding
Reconstruction Algorithms – Quick Comparison
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FBP: Analytical solution → fast → 1/r correction with ramp filter → noise-sensitive → streak artefacts → may produce negative values → limited modelling of physical factors → limited use today
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MLEM: Iterative → Poisson statistics → multiplicative update → no negative values → all projection data in every iteration → very slow → not suitable for clinical use
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OSEM: Accelerated version of MLEM → division into subsets → acceleration ≈ number of subsets → standard today → typical: 2-4 iterations × 8-16 subsets
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Effective iterations = number of iterations × number of subsets
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Iterations↑ → resolution↑, contrast↑, noise↑
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Iterations↓ → noise↓, resolution↓, contrast↓
Attenuation Correction – Quick Comparison
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Chang: Post-reconstruction → uniform µ assumption → simple → specific to SPECT → inaccurate in the thorax (lung–soft tissue difference)
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CTAC: Intra-reconstruction → non-uniform µ map → CT HU → bilinear conversion → voxel-based → most accurate → standard in PET/CT and SPECT/CT
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Transmission source: Ge-68 or Cs-137 → old PET method → no longer used
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MRAC: In PET/MR → Dixon segmentation → bone problem → solved with UTE/ZTE/atlas/deep learning
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Attenuation correction is mandatory in PET (photon pair attenuation, independent of source position)
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Attenuation correction is recommended in SPECT but not mandatory
PET attenuation correction factor: ACF = e^(+µ·D) → independent of source position
Golden Rules
1. The standard reconstruction algorithm in SPECT and PET today → OSEM 2. Attenuation correction in PET → mandatory (CTAC standard) 3. Attenuation correction in SPECT → recommended (Chang or CTAC) 4. SPECT scatter correction → TEW 5. PET scatter correction → SSS 6. Most common filter → Butterworth 7. Number of frames in gated SPECT → 8 or 16 8. Most stable phase in respiratory gating → end-expiration 9. Artefact of PSF modelling → Gibbs ringing 10. Point source in the sinogram → sinusoidal curve
Current guidelines on this chapter's topics
The latest guidelines and consensus documents on the procedures covered in this chapter (official EANM index and primary sources, November 2026). Comparison of the text with these versions is in progress; consult the guideline itself for details.
The detector rotates around the patient; at each angle the sum of all activity along that direction (line integral) gives a projection profile. Stacking the profiles in angle order gives the sinogram. A point source at the centre is seen in the same place at every angle and draws a straight vertical line; an off-centre point draws a sine curve, hence the name.
Object:
The calculations are real: 64 × 64 matrix, projections over 360° (parallel beam), ramp (Ram-Lak) filter, MLEM/OSEM. The phantom has a body, two hot lesions and one cold region. Noisy data have Poisson noise added; total counts are schematic.
Step 1/2
Simple back projection
Each projection is smeared back into the image along its direction and all are summed. With few angles a star artefact appears around a point source; as the number of angles increases the star turns into a blur that falls off with distance (1/r). Change the number of projections.
Object:
Number of projections:
The calculations are real: 64 × 64 matrix, projections over 360° (parallel beam), ramp (Ram-Lak) filter, MLEM/OSEM. The phantom has a body, two hot lesions and one cold region. Noisy data have Poisson noise added; total counts are schematic.
Starting from a uniform estimate, the estimate is forward projected, compared with the measured projections and updated by the ratio. MLEM uses all projections each iteration and is slow; OSEM divides the projections into equally spaced subsets and speeds up roughly by the number of subsets (effective updates = iterations × subsets). Change the number of subsets: with more iterations contrast increases, but so does noise.
Number of subsets:
The calculations are real: 64 × 64 matrix, projections over 360° (parallel beam), ramp (Ram-Lak) filter, MLEM/OSEM. The phantom has a body, two hot lesions and one cold region. Noisy data have Poisson noise added; total counts are schematic.
Step 1/3
SPECT: depth
Photons travelling from the source to the camera pass through tissue; those absorbed or scattered on the way (×) never reach it. At 140 keV soft tissue µ ≈ 0.15 cm⁻¹ and the fraction reaching the camera is e^(−µd), so it depends on source depth: 74% from 2 cm, 11% from 15 cm. Deep structures therefore look fainter than they are. Change the depth and watch the counter. The window below shows one interaction in the body at atomic scale: at 140 keV ~98% of interactions in tissue are Compton scattering; the photon is not absorbed, it changes direction and gives part of its energy to an electron. A photon scattered through a small angle stays inside the energy window (126–154 keV) and is counted in the wrong place; this is why attenuation and scatter are corrected together.
Emitted toward camera: 0 · reached: 0 (0%)
Step 1/3
ECG gating
Each R wave is the trigger: the R-R interval is divided into equal frames (typically 8 or 16) and, beat after beat, counts from the same phase are added to the same frame, giving one image per phase (a cine loop). In the short-axis section the left ventricular cavity shrinks in systole and the wall thickens. EDV is usually frame 1 and ESV frame 3-4 of 8; LVEF = (EDV − ESV)/EDV. With 16 frames temporal sampling is better and the smallest volume is captured more accurately.
The body cross-section is elliptical. On a circular orbit the radius is set by the widest part, so the detector stays far from the body anteriorly and posteriorly; the parallel-hole collimator's resolution worsens with distance. On a body-contour orbit the detector stays close at every angle and the mean resolution improves.