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/spl deg/ 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 and approximate rebinning algorithms for 3-D PET data

In emission tomography statistically based iterative methods can improve image quality relative to analytic image reconstruction through more accurate physical and statistical modelling of high-energy photon production and detection processes. Continued exponential improvements in computing power, coupled with the development of fast algorithms, have made routine use of iterative techniques practical, resulting in their increasing popularity in both clinical and research environments. Here we review recent progress in developing statistically based iterative techniques for emission computed tomography. We describe the different formulations of the emission image reconstruction problem and their properties. We then describe the numerical algorithms that are used for optimizing these functions and illustrate their behaviour using small scale simulations.

https://iopscience.iop.org/article/10.1088/0031-9155/51/15/R01/pdf

Iterative reconstruction techniques in emission computed tomography.

The PENN-PET scanner consists of six hexagonally arranged position-sensitive Nal(TI) detectors. This design offers high spatial resolution in all three dimensions, high sampling density along all three axes without scanner motion, a large axial acceptance angle, good energy resolution, and good timing resolution. This results in three-dimensional imaging capability with high sensitivity and low scatter and random backgrounds. The spatial resolution is 5.5 mm (FWHM) in all directions near the center. The true sensitivity, for a brain-sized object, is a maximum of 85 kcps/microCi/ml and the scatter fraction is a minimum of 10%, both depending on the lower level energy threshold. The scanner can handle up to 5 mCi in the field of view, at which point the randoms equal the true coincidences and the detectors reach their count rate limit. We have so far acquired [18F]FDG brain studies and cardiac studies, which show the applicability of our scanner for both brain and whole-body imaging. With the results to date, we feel that this design results in a simple yet high performance scanner which is applicable to many types of static and dynamic clinical studies.

https://jnm.snmjournals.org/content/31/5/617.full.pdf

Continuous-slice PENN-PET: a positron tomograph with volume imaging capability.

The art of medical computed tomography is constantly evolving and the last years have seen new ground breaking systems with multi-row detectors. These tomographs are able to increase both scanning ...

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Cone-Beam Reconstruction Using Filtered Backprojection

Emission computed tomography (ECT) is a technology for medical imaging whose importance is increasing rapidly. There is a growing appreciation for the value of the functional (as opposed to anatomical) information that is provided by ECT and there are significant advancements taking place, both in the instrumentation for data collection, and in the computer methods for generating images from the measured data. These computer methods are designed to solve the inverse problem known as "image reconstruction from projections". This paper uses the various models of the data collection process as the framework for presenting an overview of the wide variety of methods that have been developed for image reconstruction in the major subfields of ECT, which are positron emission tomography (PET) and single-photon emission computed tomography (SPECT). The overall sequence of the major sections in the paper, and the presentation within each major section, both proceed from the more realistic and general models to those that are idealized and application specific. For most of the topics, the description proceeds from the three-dimensional case to the two-dimensional case. The paper presents a broad overview of algorithms for PET and SPECT, giving references to the literature where these algorithms and their applications are described in more detail.

Overview of methods for image reconstruction from projections in emission computed tomography

The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel-ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections. The values of these coefficients may be plotted on a two-dimensional map whose coordinates are spatial frequency w (continuous) and angular harmonic number n (discrete). For |w| large, the Fourier coefficients on the line n=kw of slope k through the origin of the coefficient space are found to depend strongly on the contributions to the projection data that, for each view, come from a certain distance to the detector plane, where the distance is a linear function of k. The values of these coefficients depend only weakly on contributions from other distances from the detector. The theoretical basis of this property is presented in this paper and a potential application to emission computerized tomography is discussed.

Novel Properties Of The Fourier Decomposition Of The Sinogram

A method is described for preprocessing projection data prior to image reconstruction in single-photon emission computed tomography. The projection data of the desired spatial distribution of emission activity is blurred by the point-response function of the collimator that is used to define the range of directions of gamma-ray photons reaching the detector. The point-response function of the collimator is not stationary, but depends on the distance from the collimator to the point. Conventional methods for deblurring collimator projection data are based on approximating the actual depth-dependent point-response function by a spatially-invariant blurring function, so that deconvolution methods can be applied independently to the data at each angle of view. The method described in this paper is based on Fourier analysis of the multi-angular data set as a whole, using special depth-dependent characteristics of the Fourier coefficients to achieve spatially-variant inverse filtering of the data in all views simultaneously. Preliminary results are presented for simulated data with a simple collimator model.

Paul R. Edholm

Papers

Novel Properties Of The Fourier Decomposition Of The Sinogram

Fourier Method For Correction Of Depth-Dependent Collimator Blurring