Resolution improvement and noise reduction in human pinhole SPECT using a multi-ray approach and the SHINE method.

PURPOSE: This work aimed at quantifying the gains in spatial resolution and noise that could be achieved when using resolution modelling based on a multi-ray approach and additionally the Statistical and Heuristic Noise Extraction (SHINE) method in human pinhole single photon emission tomography (PH-SPECT). METHODS: PH-SPECT of two line phantoms and one homogeneous cylinder were recorded using parameters suited for studies of the human neck area. They were reconstructed using pinhole dedicated ordered subsets expectation maximisation algorithm including a resolution recovery technique based on 7 or 21 rays. Optionally, the SPECT data were SHINE pre-processed. Transverse and axial full widths at half-maximum (FWHM) were obtained from the line phantoms. The noise was quantified using the coefficient of variation (COV) derived from the uniform phantom. Two human PH-SPECT studies of the thyroid (a hot nodule and a very low uptake) were processed with the same algorithms. RESULTS: Depending on the number of iterations, FWHM decreased by 30 to 50% when using the multi-ray approach in the reconstruction process. The SHINE method did not affect the resolution but decreased the COV by at least 20% and by 45% when combined with the multi-ray method. The two human studies illustrated the gain in spatial resolution and the decrease in noise afforded both by the multi-ray reconstruction and the SHINE method. CONCLUSION: Iterative reconstruction with resolution modelling allows to obtain high resolution human PH-SPECT studies with reduced noise content. The SHINE method affords an additional noise reduction without compromising the resolution.

Single and multipinhole collimator design evaluation method for small animal SPECT.

High-resolution functional imaging of small animals is often obtained by single pinhole SPECT with circular orbit acquisition. Multipinhole SPECT adds information due to its improved sampling, and can improve the trade-off between resolution and sensitivity. To evaluate different pinhole collimator designs an efficient method is needed that quantifies the reconstruction image quality. In this paper, we propose a fast, approximate method that examines the quality of individual voxels of a postsmoothed maximum likelihood expectation maximization (MLEM) reconstruction by studying their linearized local impulse response (LLIR) and (co)variance for a predefined target resolution. For validation, the contrast-to-noise ratios (CNRs) in some voxels of a homogeneous sphere and of a realistic rat brain software phantom were calculated for many single and multipinhole designs. A good agreement was observed between the CNRs obtained with the approximate method and those obtained with postsmoothed MLEM reconstructions of simulated noisy projections. This good agreement was quantified by a least squares fit through these results, which yielded a line with slope 1.02 (1.00 expected) and a y-intercept close to zero (0 expected). 95.4% of the validation points lie within three standard deviations from that line. Using the approximate method, the influence on the CNR of varying a parameter in realistic single and multipinhole designs was examined. The investigated parameters were the aperture diameter, the distance between the apertures and the axis-of-rotation, the focal distance, the acceptance angle, the position of the apertures, the focusing distance, and the number of pinholes. The results can generally be explained by the change in sensitivity, the amount of postsmoothing, and the amount of overlap in the projections. The method was applied to multipinhole designs with apertures focusing at a single point, but is also applicable to other designs.

SOLVING THE INTERIOR PROBLEM OF COMPUTED TOMOGRAPHY USING A PRIORI KNOWLEDGE.

The case of incomplete tomographic data for a compactly supported attenuation function is studied. When the attenuation function is a priori known in a subregion, we show that a reduced set of measurements is enough to uniquely determine the attenuation function over all the space. Furthermore, we found stability estimates showing that reconstruction can be stable near the region where the attenuation is known. These estimates also suggest that reconstruction stability collapses quickly when approaching the set of points that are viewed under less than 180 degrees. This paper may be seen as a continuation of the work "Truncated Hilbert transform and Image reconstruction from limited tomographic data" that was published in Inverse Problems in 2006. This continuation tackles new cases of incomplete data that could be of interest in applications of computed tomography.

Penalized maximum-likelihood sinogram restoration for dual focal spot computed tomography.

Due to various system non-idealities, the raw data generated by a computed tomography (CT) machine are not readily usable for reconstruction. Although the deterministic nature of corruption effects such as crosstalk and afterglow permits correction by deconvolution, there is a drawback because deconvolution usually amplifies noise. Methods that perform raw data correction combined with noise suppression are commonly termed sinogram restoration methods. The need for sinogram restoration arises, for example, when photon counts are low and non-statistical reconstruction algorithms such as filtered backprojection are used. Many modern CT machines offer a dual focal spot (DFS) mode, which serves the goal of increased radial sampling by alternating the focal spot between two positions on the anode plate during the scan. Although the focal spot mode does not play a role with respect to how the data are affected by the above-mentioned corruption effects, it needs to be taken into account if regularized sinogram restoration is to be applied to the data. This work points out the subtle difference in processing that sinogram restoration for DFS requires, how it is correctly employed within the penalized maximum-likelihood sinogram restoration algorithm and what impact it has on image quality.

Automatic determination of left ventricular ejection fraction from gated blood-pool tomography.

UNLABELLED: The aim of this study was to develop and validate a new algorithm to automatically compute left ventricular ejection fraction (LVEF) from gated blood-pool tomography (GBPT). The results were compared with those of conventional planar radionuclide angiocardiography (PRNA). METHODS: Fifty-three consecutive patients received an injection of 740 MBq (99m)Tc-labeled human serum albumin. PRNA and GBPT were performed consecutively in a random sequence. PRNA served as the reference, and GBPT images were processed using a new edge detection algorithm. The algorithm is fast (<45 s), fully automatic, and works in three-dimensional space. The method includes identification of the valve plane and the septum. The left ventricular cavity at end-diastole is delineated by segmentation using an iterative threshold technique. An optimal threshold is reached when the corresponding isocontour best fits the first derivative of the end-diastolic count distribution in three dimensions. This optimal threshold is then applied to delineate the left ventricular cavity on the other time bins. The data are corrected for the partial-volume effect. Left ventricular volumes are determined using a geometry-based method and are used to calculate the ejection fraction. RESULTS: The success rate of the new algorithm was 94%. LVEFs calculated from GBPT agreed well with those calculated from PRNA (r = 0.78; GBPT = 0.94 PRNA + 6.33). The systematic error was 2.8%, and the random error was 8.8%. Excellent inter- and intraobserver reproducibility was found, with average differences of 1.1% +/- 4.6% and 1.1% +/- 5.0%, respectively, between the two measurements. CONCLUSION: This new algorithm provides a fast, automated, and objective method to calculate LVEF from GBPT.

A rotating PET scanner using BGO block detectors: design, performance and applications.

Recent advances in fully three-dimensional reconstruction for multi-ring PET scanners have led us to explore the potential of a prototype scanner based on the rotation of two opposing arrays of BGO block detectors. The prototype contains only one-third of the number of detectors in the equivalent full ring scanner, resulting in reduced cost. With a lower energy threshold at 250 keV, the absolute efficiency of the scanner is 0.5% and the scatter fraction is 35% for a 20-cm cylinder. Transaxial and axial spatial resolution is about 6 mm. The maximum noise equivalent count rate estimated for a 15-cm diameter cylinder is 36,000 cps at a concentration of 26 kBq/ml. The minimum scan time for a 18F-fluoro-2-deoxyglucose (FDG) brain study is 55 sec. The camera has been validated for clinical applications using both FDG and 82Rb.

Three-dimensional multimodality medical image registration using a parameter accumulation approach.

A parameter accumulation method based on the Hough transformation is proposed to register three-dimensional (3-D) multimodality medical images. The estimation of registration parameters is decomposed into separate estimations of rotation, using directional vectors, and translation, using positional vectors. Similarly, the rotation parameters are decomposed into the rotation axis and angle, which are then estimated separately. This kind of decomposition reduces the parametric dimension and improves the computing efficiency which has been a major concern in implementing the Hough transformation. When 3-D rotation is involved, evaluating registration error is not straightforward. This paper introduces an equivalent error angle as a criterion to evaluate the performance of 3-D registration methods. Experimental results indicate that a least-squares fitting is superior to the parameter accumulation with data contaminated by additive noise only. When mismatched feature points (outliers) exist in the data set, however, the parameter accumulation approach is more accurate. The application of the proposed approach to the registration of 3-D PET and CT images is demonstrated.

A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection.

An exact inversion formula written in the form of shift-variant filtered-backprojection (FBP) is given for reconstruction from cone-beam data taken from any orbit satisfying H.K. Tuy's (1983) sufficiency conditions. The method is based on a result of P. Grangeat (1987), involving the derivative of the three-dimensional (3D) Radon transform, but unlike Grangeat's algorithm, no 3D rebinning step is required. Data redundancy, which occurs when several cone-beam projections supply the same values in the Radon domain, is handled using an elegant weighting function and without discarding data. The algorithm is expressed in a convenient cone-beam detector reference frame, and a specific example for the case of a dual orthogonal circular orbit is presented. When the method is applied to a single circular orbit (even though Tuy's condition is not satisfied), it is shown to be equivalent to the well-known algorithm of L.A. Feldkamp et al. (1984).

Quasi-exact filtered backprojection algorithm for long-object problem in helical cone-beam tomography.

Exact reconstruction from axially truncated cone-beam projections acquired with a helical vertex path is a challenging problem for which solutions are currently under investigation by some researchers. This paper deals with a difficult class of this problem called the long-object problem. Its purpose is to reconstruct a central region of interest (ROI) of a long object when the helical path extends only a little bit above and below the ROI. By extending the authors' recent approach based on the triangular decomposition of the Grangeat formula, we derive quasi-exact reconstruction algorithms whose overall structure is of filtered backprojection (FBP) style. Unlike the previous similar approaches to the long-object problem, the proposed FBP algorithms do not require additional two circular scans at the ends of the helical path. Furthermore, the algorithms require a significantly smaller detector area and achieve improved image quality even for a large pitch compared with the approximate Feldkamp algorithms. One drawback of the proposed algorithms is the computational time, which is much longer than for the Feldkamp algorithms. We show some simulation results to demonstrate the performances of the proposed algorithms.

An algorithm for three-dimensional reconstruction incorporating cross-plane rays.

Conventional multislice positron cameras reconstruct a three-dimensional distribution of a positron-emitting radioscope as a set of two-dimensional transverse sections. Consequently, annihilation photons which cross two or more planes are eliminated from the data. Such an approach makes efficient use of the emitted photon flux. A method is proposed which makes more efficient use of the available photons by including both oblique and transverse section in the reconstruction. The implementation of the method consists of centering a scaled convolution filter on each detected coincidence event line and backprojecting the filter values through the three-dimensional reconstruction volume. The final image is normalized to allow for the different number of oblique and transverse sections that contribute to each point in the imaging volume. The method has been evaluated using both simulated data and measured data obtained with a routing area detector positron camera.

Fast fully 3-D image reconstruction in PET using planograms.

We present a method of performing fast and accurate three-dimensional (3-D) backprojection using only Fourier transform operations for line-integral data acquired by planar detector arrays in positron emission tomography. This approach is a 3-D extension of the two-dimensional (2-D) linogram technique of Edholm. By using a special choice of parameters to index a line of response (LOR) for a pair of planar detectors, rather than the conventional parameters used to index a LOR for a circular tomograph, all the LORs passing through a point in the field of view (FOV) lie on a 2-D plane in the four-dimensional (4-D) data space. Thus, backprojection of all the LORs passing through a point in the FOV corresponds to integration of a 2-D plane through the 4-D "planogram." The key step is that the integration along a set of parallel 2-D planes through the planogram, that is, backprojection of a plane of points, can be replaced by a 2-D section through the origin of the 4-D Fourier transform of the data. Backprojection can be performed as a sequence of Fourier transform operations, for faster implementation. In addition, we derive the central-section theorem for planogram format data, and also derive a reconstruction filter for both backprojection-filtering and filtered-backprojection reconstruction algorithms. With software-based Fourier transform calculations we provide preliminary comparisons of planogram backprojection to standard 3-D backprojection and demonstrate a reduction in computation time by a factor of approximately 15.

Exact and approximate rebinning algorithms for 3-D PET data.

This paper presents two new rebinning algorithms for the reconstruction of three-dimensional (3-D) positron emission tomography (PET) data. A rebinning algorithm is one that first sorts the 3-D data into an ordinary two-dimensional (2-D) data set containing one sinogram for each transaxial slice to be reconstructed; the 3-D image is then recovered by applying to each slice a 2-D reconstruction method such as filtered-backprojection. This approach allows a significant speedup of 3-D reconstruction, which is particularly useful for applications involving dynamic acquisitions or whole-body imaging. The first new algorithm is obtained by discretizing an exact analytical inversion formula. The second algorithm, called the Fourier rebinning algorithm (FORE), is approximate but allows an efficient implementation based on taking 2-D Fourier transforms of the data. This second algorithm was implemented and applied to data acquired with the new generation of PET systems and also to simulated data for a scanner with an 18 degrees axial aperture. The reconstructed images were compared to those obtained with the 3-D reprojection algorithm (3DRP) which is the standard "exact" 3-D filtered-backprojection method. Results demonstrate that FORE provides a reliable alternative to 3DRP, while at the same time achieving an order of magnitude reduction in processing time.

Exact rebinning methods for three-dimensional PET.

The high computational cost of data processing in volume PET imaging is still hindering the routine application of this successful technique, especially in the case of dynamic studies. This paper describes two new algorithms based on an exact rebinning equation, which can be applied to accelerate the processing of three-dimensional (3-D) PET data. The first algorithm, FOREPROJ, is a fast-forward projection algorithm that allows calculation of the 3-D attenuation correction factors (ACF's) directly from a two-dimensional (2-D) transmission scan, without first reconstructing the attenuation map and then performing a 3-D forward projection. The use of FOREPROJ speeds up the estimation of the 3-D ACF's by more than a factor five. The second algorithm, FOREX, is a rebinning algorithm that is also more than five times faster, compared to the standard reprojection algorithm (3DRP) and does not suffer from the image distortions generated by the even faster approximate Fourier rebinning (FORE) method at large axial apertures. However, FOREX is probably not required by most existing scanners, as the axial apertures are not large enough to show improvements over FORE with clinical data. Both algorithms have been implemented and applied to data simulated for a scanner with a large axial aperture (30 degrees), and also to data acquired with the ECAT HR and the ECAT HR+ scanners. Results demonstrate the excellent accuracy achieved by these algorithms and the important speedup when the sinogram sizes are powers of two.

Comparison of 3-D reconstruction with 3D-OSEM and with FORE+OSEM for PET.

The combination of Fourier rebinning (FORE) and the ordered subsets expectation-maximization (OSEM), a fast statistical algorithm, appears as a promising alternative to the fully three-dimensional (3-D) iterative approach for clinical positron emission tomography (PET) data. In this paper, we evaluated the properties of FORE+OSEM and compared it with fully 3-D OSEM using both simulations and data acquired by commercial scanners. The aim is to determine to what extent the speed advantage of FORE+OSEM is paid for by a possible degradation of image quality in the case of noisy clinical PET data. A forward- and back-projection pair based on a line integral model was used in two-dimensional OSEM and 3-D OSEM (3D-OSEM) instead of a system matrix. Different variants of both approaches have been studied with simulations in terms of contrast-noise tradeoff. Two variants--FORE+OSEM with attenuation weighting (AW) [FORE+OSEM(AW)] and 3D-OSEM with attenuation-normalization weighting (ANSP) and a shifted-Poisson (SP) model [3D-OSEM(ANSP)]--were compared with measured phantom data and patient data. Based on the results from both simulations and measured data, we conclude that: 1) both attenuation (-normalization) weighting and the SP model improve the image quality but slow down the convergence and 2) despite its approximate nature, FORE+OSEM does not show apparent image degradation compared with 3D-OSEM for data with a noise level typical of a whole-body FDG scan.

Fully three-dimensional reconstruction for a PET camera with retractable septa.

A fully 3-D reconstruction algorithm has been developed to reconstruct data from a 16 ring PET camera (a Siemens/CTI 953B) with automatically retractable septa. The tomograph is able to acquire coincidences between any pair of detector rings and septa retraction increases the total system count rate by a factor of 7.8 (including scatter) and 4.7 (scatter subtracted) for a uniform, 20 cm diameter cylinder. The reconstruction algorithm is based on 3-D filtered backprojection, expressed in a form suitable for the multi-angle sinogram data. Sinograms which are not measured due to the truncated cylindrical geometry of the tomograph, but which are required for a spatially invariant response function, are obtained by forward projection. After filtering, the complete set of sinograms is backprojected into a 3-D volume of 128x128x31 voxels using a voxel-driven procedure. The algorithm has been validated with simulation, and tested with both phantom and clinical data from the 953B.

Filtered backprojection reconstruction of combined parallel beam and cone beam SPECT data.

The reconstruction problem for a combined parallel beam (PB) and cone beam (CB) imaging geometry has been addressed. The general algorithm (CB-FBP) of Defrise and Clack has been applied to this geometry and shown to provide accurate images as expected. A second algorithm specifically tailored to the PB-CB geometry was developed. It uses the general principles of the CB-FBP method to combine a shift-variant filtering of the PB data with a standard reconstruction of the CB data using the algorithm of Feldkamp, Davis and Kress (FDK). This 'mixed' algorithm has the advantage of fewer interpolation steps, thereby reducing reconstruction time and providing more accurate reconstructions. The algorithms were applied to noiseless data from a computer-generated 3D Shepp phantom. Both the CB-FBP algorithm and the mixed algorithm successfully combine the CB and the PB data to correct the well known artefacts observed when reconstructing CB data acquired with a circular orbit. The mixed algorithm is about twice as fast as CB-FBP and results in better image quality, due to decreased discretization errors. However, the two algorithms yield comparable image quality when applied to a disc phantom measured with a two-headed SPECT system.

A solution to the long-object problem in helical cone-beam tomography.

This paper presents a new algorithm for the long-object problem in helical cone-beam (CB) computerized tomography (CT). This problem consists in reconstructing a region-of-interest (ROI) bounded by two given transaxial slices, using axially truncated CB projections corresponding to a helix segment long enough to cover the ROI, but not long enough to cover the whole axial extent of the object. The new algorithm is based on a previously published method, referred to as CB-FBP (Kudo et al 1998 Phys. Med. Biol. 43 2885-909), which is suitable for quasi-exact reconstruction when the helix extends well beyond the support of the object. We first show that the CB-FBP algorithm simplifies dramatically, and furthermore constitutes a solution to the long-object problem, when the object under study has line integrals which vanish along all PI-lines. (A PI line is a line which connects two points of the helix separated by less than one pitch.) Exploiting a geometric property of the helix, we then show how the image can be expressed as the sum of two images, where the first image can be reconstructed from the measured CB projections by a simple backprojection procedure, and the second image has zero PI-line integrals and hence can be reconstructed using the simplified CB-FBP algorithm. The resulting method is a quasi-exact solution to the long-object problem, called the ZB method. We present its implementation and illustrate its performance using simulated CB data of the 3D Shepp phantom and of a more challenging head-like phantom.

Cone-beam filtered-backprojection algorithm for truncated helical data.

This paper investigates 3D image reconstruction from truncated cone-beam (CB) projections acquired with a helical vertex path. First, we show that a rigorous derivation of Grangeat's formula for truncated projections leads to a small additional term compared with previously published similar formulations. This correction term is called the boundary term. Next, this result is used to develop a CB filtered-backprojection (FBP) algorithm for truncated helical projections. This new algorithm only requires the CB projections to be measured within the region that is bounded, in the detector, by the projections of the upper and lower turns of the helix. Finally, simulations with mathematical phantoms demonstrate that: (i) the boundary term is necessary to obtain high-quality imaging of low-contrast structures and (ii) good image quality is obtained even with large values of the pitch of the helix.

Single-slice rebinning method for helical cone-beam CT.

In this paper, we present reconstruction results from helical cone-beam CT data, obtained using a simple and fast algorithm, which we call the CB-SSRB algorithm. This algorithm combines the single-slice rebinning method of PET imaging with the weighting schemes of spiral CT algorithms. The reconstruction is approximate but can be performed using 2D multislice fan-beam filtered backprojection. The quality of the results is surprisingly good, and far exceeds what one might expect, even when the pitch of the helix is large. In particular, with this algorithm comparable quality is obtained using helical cone-beam data with a normalized pitch of 10 to that obtained using standard spiral CT reconstruction with a normalized pitch of 2.

Implementation of three-dimensional image reconstruction for multi-ring positron tomographs.

In view of the number of PET studies involving low count rate acquisitions, there has been increasing interest recently in the development of positron cameras capable of fully three-dimensional acquisition and reconstruction. This interest has given impetus to the study of algorithms for 3D reconstruction, including those algorithms suitable for application to multi-ring PET scanners. While 2D reconstruction methods can often be generalised to 3D, a number of implementation problems arise which are unique to the 3D approach. This paper examines some of the difficulties associated with the generalisation of the filtered backprojection algorithm to 3D, paying particular attention to the approximations and variable transformations required for application to data from a multi-ring scanner.