Iterative and analytical reconstruction algorithms for varying-focal-length cone-beam projections

The iterative maximum-likelihood expectation-maximization (ML-EM) algorithm is an excellent algorithm for image reconstruction and usually provides better images than the filtered backprojection (FBP) algorithm. However, a windowed FBP algorithm can outperform the ML-EM in certain occasions, when the least-squared difference from the true image, that is, the least-squared error (LSE), is used as the comparison criterion. Computer simulations were carried out for the two algorithms. For a given data set the best reconstruction (compared to the true image) from each algorithm was first obtained, and the two reconstructions are compared. The stopping iteration number of the ML-EM algorithm and the parameters of the windowed FBP algorithm were determined, so that they produced an image that was closest to the true image. However, to use the LSE criterion to compare algorithms, one must know the true image. How to select the optimal parameters when the true image is unknown is a practical open problem. For noisy Poisson projections, computer simulation results indicate that the ML-EM images are better than the regular FBP images, and the windowed FBP algorithm images are better than the ML-EM images. For the noiseless projections, the FBP algorithms outperform the ML-EM algorithm. The computer simulations reveal that the windowed FBP algorithm can provide a reconstruction that is closer to the true image than the ML-EM algorithm.

The purpose of this article is to study the added value of model-based iterative reconstruction (MBIR) on metal artifact reduction on CT compared with standard filtered back projection (FBP). Ex vivo imaging was performed on several metal implants. Datasets were reconstructed with standard FBP and MBIR algorithms. The sizes of the artifacts surrounding the metal implant were recorded and compared. In vivo imaging was performed on 62 patients with metal implants. Each dataset was reconstructed with FBP and MBIR algorithms. Objective image quality was assessed by measuring the size of the artifact generated by the metal implant. Subjective image quality was graded on a 3-point scale, taking into account the visibility of the bone-metal interface, as well as the visibility of the neighboring soft tissues. Ex vivo analysis yielded a reduction of 82% in the size of the artifact when using the MBIR algorithm, compared with the FBP algorithm. The mean (SD) size of the artifacts was 1.4 ± 0.8 and 0.25 ± 0.06 cm(2) with FBP and MBIR, respectively. In vivo, the mean size of the artifacts decreased from 7.3 ± 1.5 cm(2) to 4.0 ± 0.9 cm(2) for FBP and MBIR, respectively (p = 0.012). The subjective image quality analysis showed an equal or better bone-metal interface of MBIR algorithm in 85% of cases. Visibility of the soft tissue surrounding the metal implant was determined to be equal or better in 97% of cases in which MBIR was used. This study shows that the MBIR algorithm allows a clear reduction of metal artifacts on CT images and, hence, a better analysis of the soft tissue surrounding the metal implant compared with FBP.

The existing communication model of SPECT studies is extended by including the attenuating medium in the communication channel. Based on the extended model two fundamental theorems are presented to demonstrate the significance of the mutual information in system design and imaging reconstruction. In addition, the authors present a mutual information formula for SPECT systems to image radionuclide distributions in attenuating objects using single photon emission computed tomography (SPECT) collimators, The formula is, in turn, expressed in terms of the source distribution, attenuation coefficients, and collimator parameters such as collimator thickness, hole size, septal thickness, hole shape factor, and focal length. The polyhedral collimator is employed for the authors' mutual information analysis in this report. Based on imaging surface decomposition, the analysis of the polyhedral collimator is reduced to the analysis of a single-headed collimator for planar imaging. Conventional collimators including parallel and cone beam collimators are used for the analysis of the single-headed collimator. The information loss due to attenuation is evaluated for myocardial imaging using technetium-99m and thalium-201.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

To intraindividually compare a low-tube voltage, low-contrast material dose computed tomography (CT) reconstructed with iterative reconstruction (IR) algorithm at standard tube voltage reconstructed with filtered back projection (FBP) and standard-contrast material dose during liver dynamic CT. Twenty-five patients with liver cirrhosis underwent 64-section multidetector CT. One hundred twenty kilovolt (peak) (kV[p]) with standard contrast material dose of 600 mg of iodine per kilogram (protocol A) and 80 kV(p) with low-contrast material dose of 450 mg of iodine per kilogram (protocol B) CT image sets were reconstructed by using FBP algorithm and that of using IR algorithm with a 60%/40% blend of IR-FBP reconstruction at 80-kV(p) image set (protocol C). Scans obtained during 3 hepatic phases were subjected to quantitative and qualitative analysis. The mean radiation dose and the contrast medium dose were significantly lower under protocols B and C than under protocol A. In all hepatic phases, all signal-to-noise and contrast-to-noise ratios were greater under protocol C than under other protocols at all anatomic sites. Qualitative analysis showed that image noise and diagnostic acceptability were significantly higher under protocol C. In all hepatic phases, a low-tube voltage, low-contrast material dose CT with IR algorithm yielded better contrast enhancement and image quality than a standard tube voltage, standard contrast material dose CT with FBP in thin adult patients.

Filtered back-projection (FBP) is the most commonly used reconstruction method for PET images, which are usually noisy. The iterative reconstruction segmented attenuation correction (IRSAC) algorithm improves image quality without reducing image resolution. The standardized uptake value (SUV) is the most clinically utilized quantitative parameter of [fluorine-18]fluoro-2-deoxy-D-glucose (FDG) accumulation. The objective of this study was to obtain a table of SUVs for several normal anatomical structures from both routinely used FBP and IRSAC reconstructed images and to compare the data obtained with both methods. Twenty whole-body PET scans performed in consecutive patients with proven or suspected non-small cell lung cancer were retrospectively analyzed. Images were processed using both IRSAC and FBP algorithms. Nonquantitative or gaussian filters were used to smooth the transmission scan when using FBP or IRSAC algorithms, respectively. A phantom study was performed to evaluate the effect of different filters on SUV. Maximum and average SUVs (SUVmax and SUVavg) were calculated in 28 normal anatomical structures and in one pathological site. The phantom study showed that the use of a nonquantitative smoothing filter in the transmission scan results in a less accurate quantification and in a 20% underestimation of the actual measurement. Most anatomical structures were identified in all patients using the IRSAC images. On average, SUVavg and SUVmax measured on IRSAC images using a gaussian filter in the transmission scan were respectively 20% and 8% higher than the SUVs calculated from conventional FBP images. Scatterplots of the data values showed an overall strong relationship between IRSAC and FBP SUVs. Individual scatterplots of each site demonstrated a weaker relationship for lower SUVs and for SUVmax than for higher SUVs and SUVavg. A set of reference values was obtained for SUVmax and SUVavg of normal anatomical structures, calculated with both IRSAC and FBP image reconstruction algorithms. The use of IRSAC and a gaussian filter for the transmission scan seems to give more accurate SUVs than are obtained from conventional FBP images using a nonquantitative filter for the transmission scan.

This paper presents an analysis of two cone beam configurations (having focal lengths of 40 and 60 cm) for the acquisition of single photon emission computed tomography (SPECT) projection data. A three-dimensional filtered backprojection algorithm is used to reconstruct SPECT images of cone beam projection data obtained using Monte Carlo simulations. The mathematical analysis resulted in on-axis point source sensitivities (calculated for a distance of 15 cm from the collimator surface) for cone beam configurations that were 1.4-3 times the sensitivities of parallel-hole and fan beam geometries having similar geometric resolutions. Cone beam collimation offers the potential for improved sensitivity for SPECT devices using large-field-of-view scintillation cameras.

The imaging of distributed sources with near-field coded aperture (CA) remains extremely challenging and is broadly considered unsuitable for single-photon emission computerized tomography (SPECT). This study proposes a novel CA SPECT reconstruction approach and evaluates the feasibilities of imaging and reconstructing distributed hot sources and cold lesions using near-field CA collimation and iterative image reconstruction. Computer simulations were designed to compare CA and pinhole collimations in two-dimensional radionuclide imaging. Digital phantoms were created and CA images of the phantoms were reconstructed using maximum likelihood expectation maximization (MLEM). Errors and the contrast-to-noise ratio (CNR) were calculated and image resolution was evaluated. An ex vivo rat heart with myocardial infarction was imaged using a micro-SPECT system equipped with a custom-made CA module and a commercial 5-pinhole collimator. Rat CA images were reconstructed via the three-dimensional (3-D) MLEM algorithm developed for CA SPECT with and without correction for a large projection angle, and 5-pinhole images were reconstructed using the commercial software provided by the SPECT system. Phantom images of CA were markedly improved in terms of image quality, quantitative root-mean-squared error, and CNR, as compared to pinhole images. CA and pinhole images yielded similar image resolution, while CA collimation resulted in fewer noise artifacts. CA and pinhole images of the rat heart were well reconstructed and the myocardial perfusion defects could be clearly discerned from 3-D CA and 5-pinhole SPECT images, whereas 5-pinhole SPECT images suffered from severe noise artifacts. Image contrast of CA SPECT was further improved after correction for the large projection angle used in the rat heart imaging. The computer simulations and small-animal imaging study presented herein indicate that the proposed 3-D CA SPECT imaging and reconstruction approaches worked reasonably well, demonstrating the feasibilities of achieving high sensitivity and high resolution SPECT using near-field CA collimation.

The maximum likelihood expectation maximisation (ML-EM) algorithm can be used to reduce reconstruction artefacts produced by filtered backprojection (FBP) methods in pinhole single-photon emission tomography (SPET). However, ML-EM suffers from noise propagation along iterations, which leads to quantitatively unpleasant reconstruction results. To avoid this increase in noise, the median root prior (MRP) algorithm for pinhole SPET was implemented. Projection data of a line source and Picker's thyroid phantom were collected using a single-head gamma camera with a pinhole collimator. MRP was added to existing pinhole ML-EM reconstruction algorithm and the phantom studies were reconstructed using MRP, ML-EM and FBP for comparison. Coefficients of variation, contrasts and full-widths at half-maximum were calculated and showed a clear reduction in noise without significant loss of resolution or decrease in contrast when MRP was applied. MRP also produced visually pleasing images even with high iteration numbers, free of the checkerboard-type noise patterns which are typical of ML-EM images.

We investigated the spatial resolution and quantitative properties of SPECT images reconstructed using filteredbackprojection (FB) and maximum likelihood-expectation maximization (ML-EM) algorithms. We studied ML-EM as a function of iteration number and projectorhackprojector (php) model, and FE3 as a function of filter. To quantify the image resolution for a shift-variant process we defined a local point response function (PRF). To justify the use of the local PRF to quantify resolution for nonlinear ML-EM we tested the regime over which the algorithm behaved linearly with respect to input perturbations. Using Fourier domain analogs of the local PRF we demonstrated that ML-EM with an accurate php can lead to images of better resolution than FB with a Butterworth or Metz filter or ML-EM with a php that does not fully model the imaging process. We also showed that the resolution improves with increasing MLEM iteration number, and the extent of the improvement depends on the accuracy of the php model. We conclude that the local PRF can be used to characterize spatial resolution in SPECT images, and that ML-EM offers the possibility of superior resolution, particularly if the algorithm contains a good model of the imaging process.

Emission tomography, including single-photon emission computed tomography (SPECT), requires image reconstruction from noisy and incomplete projection data. The maximum-likelihood expectation maximization (MLEM) algorithm is widely used due to its statistical foundation and non-negativity preservation, but it is highly sensitive to noise, particularly in low-count conditions. Although total variation (TV) regularization can reduce noise, it often oversmooths structural details and requires careful parameter tuning. We propose a Graph-Enhanced Expectation Maximization (GREM) algorithm that incorporates graph-based neighborhood information into an MLEM-type multiplicative reconstruction scheme. The method is motivated by a penalized formulation combining a Kullback–Leibler divergence term with a graph Laplacian regularization term, promoting local structural consistency while preserving edges. The resulting update retains the multiplicative structure of MLEM and preserves the non-negativity of the image estimates. Numerical experiments using synthetic phantoms under multiple noise levels, as well as clinical 99mTc-GSA liver SPECT data, demonstrate that GREM consistently outperforms conventional MLEM and TV-regularized MLEM in terms of PSNR and MS-SSIM. These results indicate that GREM provides an effective and practical approach for edge-preserving noise suppression in emission tomography without relying on external training data.

Quantitative assessment of regional myocardial blood flow with thallium-201 and SPECT

Low spatial resolution and the related partial volume effects limit the diagnostic potential of brain single photon emission computed tomography (SPECT) imaging. As a possible remedy for this problem we propose a technique for the fusion of SPECT and MR images, which requires for a given patient the SPECT data and the T1-weighted MR image. Basically, after the reconstruction and coregistration steps, the high-frequency part of the MR, which would be unrecoverable by the set SPECT acquisition system + reconstruction algorithm, is extracted and added to the SPECT image. The tuning of the weight of the MR on the resulting fused image can be performed very quickly, any iterative reconstruction algorithm can be used and, in the case that the SPECT projections are not available, the proposed technique can also be applied directly to the SPECT image, provided that the performance of the scanner is known. The procedure has the potential of increasing the diagnostic value of a SPECT image. Even in the locations of SPECT-MR mismatch it does not significantly affect quantitation over regions of interest (ROIs) whose dimensions are decidedly larger than the SPECT resolution distance. On the other hand, appreciable corrections for partial volume effects are expected in the locations where the contrast in the structural MR matches the corresponding contrast in functional activity.

This work is aimed at evaluating the image reconstruction techniques used in single photon emission computed tomography (SPECT/CT) imaging. The reconstruction techniques considered in this work are: the ordered subset expectation maximization (OSEM) and the Filtered Back Projection (FBP). An anthropomorphic torso phantom with lung and liver inserts was injected with 99mTc. The liver and the background were given 0.2 MBq/ml and 0.07 MBq/ml respectively. The lungs inserts were filled with polystyrene beads for humanization. A mimicked 30 ml tumor (27 mm) in the liver insert was given 2 MBq/ml sequential SPECT/CT (step and shot, 10 mins over 180° per head) and CT (120 kVp, 80 mAs) projections were acquired using dual head SPECT/16 slice CT system. The projections were reconstructed using OSEM (10 subsets for 2–10 numbers of iterations, Butterworth post filtering, 10 orders and 0.48 frequencies) and FBP (using Butterworth post filtering at 10 order and cutoff frequencies of 0.38–0.58, 0.05 gaps). Image J software was used for the image analysis. Statistical t-test tested the mean gray values of the tumor and its background. The OSEM and FBP reconstructed images were evaluated from their contrast-to-noise ratio (CNR). The optimal parameter was selected based on 3–5 CNR detection range set by the Rose criterion. The t-test showed the background and the tumors mean values to be statistically significant (P ≪ 0.05). The CNR values for FBP images were all below the detection range, maximum value at the cutoff frequency 0.48 (1.69). In OSEM images at cutoff frequency 0.48, the CNR values were within the detection range for 2–8 numbers of iteration with maximum value (4.89) at 4 numbers of iteration. OSEM was found to be the best for tumor detection and administered activity can be reduced at 4 OSEM’s of iterations (40 MLEM iterations) for patient safety. Keywords: Anthropomorphic torso phantom, 99mTc, SPECT, iterative reconstruction, CNR, P-Value, liver Cite this Article F. Usman, R. Zainon, A. Saidu, A. Bala. Evaluation of image reconstruction techniques in Single photon emission computed tomography (SPECT/CT) imaging. Research & Reviews: Journal of Physics. 2016; 5(2): 13–22p.

For 2D data with Poisson noise we give explicit formulae for the optimal space-invariant Wiener-type filter with some a priori geometric restrictions on the window function. We show that, under some natural geometric condition, this restrictedly optimal Wiener-type filter admits a very efficient approximation by an approximately optimal filter with an unknown object power spectrum. Generalizations to the case of some more general noise model are also given. Proceeding from these results we (a) explain, in particular, an efficiency of some well-known ‘1D’ approximately optimal space-invariant Wiener-type filtering scheme with an unknown object power spectrum in single-photon-emission-computed tomography (SPECT) and positron emission tomography (PET) imaging based on the classical filtered back-projection (FBP) algorithm or its iterative use and (b) also propose an efficient 2D approximately optimal space-invariant Wiener-type filter with an unknown object power spectrum for SPECT imaging based on the generalized FBP algorithm (implementing the explicit formula for the nonuniform attenuation correction) and/or the classical FBP algorithm (used iteratively). An efficient space-variant version of the latter 2D filter is also announced. Numerical examples illustrating the aforementioned results in the framework of simulated SPECT imaging are given.

In this paper, the reconstruction of axisymmetric temperature and H2O concentration distributions in a flat flame burner is realized by tunable diode laser absorption spectroscopy (TDLAS) and filtered back-projection (FBP) algorithm. Two H2O absorption transitions (7154.354/7154.353 cm-1 and 7467.769 cm-1) are selected as line pair for temperature measurement, and time division multiplexing technology is adopted to scan this two H2O absorption transitions simultaneously at 1 kHz repetition rate. In the experiment, FBP algorithm can be used for reconstructing axisymmetric distributions of flow field parameters with only single view parallel-beam TDLAS measurements, and the same data sets from the given parallel beam are used for other virtual projection angles and beams scattered between 0° and 180°. The real-time online measurements of projection data, i.e., integrated absorbance both for pre-selected transitions on CH4/air flat flame burner are realized by Voigt on-line fitting, and the fitting residuals are less than 0.2%. By analyzing the projection data from different views based on FBP algorithm, the distributions of temperature and concentration along radial direction can be known instantly. The results demonstrate that the system and the proposed innovative FBP algorithm are capable for accurate reconstruction of axisymmetric temperature and H2O concentration distribution in combustion systems and facilities.