[en] There is increasing interest in reconstructing projection data directly in three dimensions. For emission tomography in particular, such a reconstruction procedure would clearly make more efficient use of the available photon flux. In the past few years, a number of authors have studied the problems associated with full three-dimensional reconstruction, especially in the case of positron tomography where three-dimensional reconstruction is likely to offer the greatest benefits. While most approaches follow that of filtered backprojection, the relationship between the various filters that have been proposed is far from evident. This paper clarifies this relationship by analysing and generalising the different classes of published filters and establishes the properties and characteristics of a general solution to the three-dimensional reconstruction problem. Some guidelines are suggested for the choice of an appropriate filter in a given situation. (author)

[en] We investigated methods to accurately reconstruct 180 degrees truncated TCT and SPECT projection data obtained from a right-angle dual-camera SPECT system for myocardial SPECT with attenuation compensation. The 180 degrees data reconstruction methods would permit substantial savings in transmission data acquisition time. Simulation data from the 3D MCAT phantom and clinical data from large patients were used in the evaluation study. Different transmission reconstruction methods including the FBP, transmission ML-EM, transmission ML-SA, and BIT algorithms with and without using the body contour as support, were used in the TCT image reconstructions. The accuracy of both the TCT and attenuation compensated SPECT images were evaluated for different degrees of truncation and noise levels. We found that using the FBP reconstructed TCT images resulted in higher count density in the left ventricular (LV) wall of the attenuation compensated SPECT images. The LV wall count density obtained using the iteratively reconstructed TCT images with and without support were similar to each other and were more accurate than that using the FBP. However, the TCT images obtained with support show fewer image artifacts than without support. Among the iterative reconstruction algorithms, the ML-SA algorithm provides the most accurate reconstruction but is the slowest. The BIT algorithm is the fastest but shows the most image artifacts. We conclude that accurate attenuation compensated images can be obtained with truncated 180 degrees data from large patients using a right-angle dual-camera SPECT system

[en] The Anger tomographic scanner (ATS) has proven to be a useful total body imaging device. ATS tomogram are longitudinal rather than transaxial, formed by focusing of activity at depth. The authors propose a new system that is based on whole body imaging gamma camera, a computer interface, and fanbeam collimator (FBC). FBC holes converge along one axis, but remain parallel along the perpendicular axis. Tomograms are achieved by moving the detector under computer control longitudinally over the patient with the FBC converging axis aligned perpendicular to the direction of motion. No latitudinal detector motion is required. A prototype was tested with a FBC designed for SPECT with a focal axis at 60 cm depth. Images were acquired in a step-and-shoot mode. A computer program was developed to reconstruct tomograms at desired depths. Tomograms of a clock phantom with 6 cm slice thicknesses were achieved with an interslice resolution of 1 cm at 8 cm depth. The authors believe a need still exists for longitudinal total body emission tomography. This system is potentially inexpensive using much of the available laboratory equipment, and is mechanically simple to implement. Shortening the FBC focal axis depth to 30 cm would greatly improve tomographic definition. Development of deconvolution algorithms would be needed to further improve tomographic definition

[en] An investigation has been conducted to develop and validate techniques for the correction of projection images in SPECT studies of the myocardium subject to misalignment due to voluntary patient motion. The problem is frequently encountered due to the uncomfortable position the patient must assume during the 30 minutes required to obtain a 180 degree set of projection images. The reconstruction of misaligned projections can lead to troublesome artifacts in reconstructed images and degrade the diagnostic potential of the procedure. Significant improvement in the quality of heart reconstructions has been realized with the implementation of an algorithm to provide detection of and correction for patient motion. Normal, involuntary motion is not corrected for, however, since such movement is below the spatial resolution of the thallium imaging system under study. The algorithm is based on a comparison of the positions of an object in a set of projection images to the known, sinusoidal trajectory of an off-axis fixed point in space. Projection alignment, therefore, is achieved by shifting the position of a point or set of points in a projection image to the sinusoid of a fixed position in space

[en] An infinite class of closed-form methods was developed by the authors last year for image reconstruction in 2D SPECT with uniform attenuation. In the work reported here, they extended their approach to develop a class of closed-form methods that compensate for the effects of both uniform attenuation and distance-dependent spatial resolution in 2D SPECT. These methods, which are characterized by an index n that can be assigned any real number, are exact in the absence of noise but propagate noise differently. They implemented this class of methods for SPECT image reconstruction in both computer-simulation and real-data studies. The results demonstrate that this class of methods corrects effectively for the aforementioned effects. Extensive computer simulation studies indicate that the method obtained with n = 2, which they had proved to be the optimal choice of n in 2D SPECT when only attenuation is present, also provides the smallest global image variance among the methods in the class when compensation for both uniform attenuation and distance-dependent spatial resolution is performed

[en] In PET, usually the data are precorrected for accidental coincidence (AC) events by real-time subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for AC events but destroys the Poisson statistics. Furthermore, for transmission tomography the weighted least-squares (WLS) method leads to systematic biases, especially at low count rates. We propose a new open-quotes shiftedclose quotes Poisson (SP) model for precorrected PET data, which properly matches the first and second order moments of the measurement statistics. Using simulations and analytic approximations, we show that estimators based on the open-quotes ordinaryclose quotes Poisson (OP) model for the precorrected data lead to higher standard deviations than the proposed method. Moreover, if one zero-thresholds the data before applying the maximization algorithm, the OP model results in systematic bias. It is shown that the proposed SP model leads to penalized-likelihood estimates free of systematic bias, even for zero-thresholded data. The proposed SP model does not increase the computation requirements compared to OP model and it is robust to errors in the estimates of the AC event rates

[en] One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. This work focuses on the application of Fourier analysis to the problem of resampling or rebinning. Conventional resampling methods utilizing some form of interpolation almost always result in a loss of resolution in the tomographic image. Fourier Transform Resampling (FTRS) offers potential improvement because the Modulation Transfer Function (MTF) of the process behaves like an ideal low pass filter. The MTF, however, is nonstationary if the coordinate transformation is nonlinear. FTRS may be viewed as a generalization of the linear coordinate transformations of standard Fourier analysis. Simulated MTF's were obtained by projecting point sources at different transverse positions in the flat fan beam detector geometry. These MTF's were compared to the closed form expression for FIRS. Excellent agreement was obtained for frequencies at or below the estimated cutoff frequency. The resulting FTRS algorithm is applied to simulations with symmetric fan beam geometry, an elliptical orbit and uniform attenuation, with a normalized root mean square error (NRME) of 0.036. Also, a Tc-99m point source study (1 cm dia., placed in air 10 cm from the COR) for a circular fan beam acquisition was reconstructed with a hybrid resampling method. The FWHM of the hybrid resampling method was 11.28 mm and compares favorably with a direct reconstruction (FWHM: 11.03 mm)

[en] Analytical expressions that describe the dependence of slopes and amplitudes of the scatter distribution functions (SDF) on source depth and media density are used to estimate a scatter component in SPECT projection data. Since the ratio of detected scattered to total photons (S/T), SDF amplitude and slope depend strongly on line source length (SL) used to obtain SDFs, we compared estimated scattered components using SDFs, obtained for lengths of 2-21 cm. At 10 cm source depth, S/T changes from 0.19 to 0.36 when SL changes from 2 to 21 cm. Scatter amplitude's dependence on source depth (d) in water was described by 6.38e^-0.186d for a 2 cm and 16.15e^-0.129d for a 21 cm SL. Slope was described by 0.292d^-0.601 for a cm SL and by 0.396d^-0.82 for a 21 cm SL. The estimated scatter components are compared with simulated SPECT projection data obtained with Monte Carlo modeling of six hot spheres placed in a cylindrical water filled phantom. The comparison of estimated with simulated total counts/projection shows very good agreement when approaching SDF for a point source (the % difference varied from 2 to 13% for 2 cm SL). Significant overestimate is seen when source length increases

[en] Smith and Grangeat derived a cone-beam inversion formula that can be applied when a nonplanar orbit satisfying the completeness condition is used. Although Grangeat's inversion formula is mathematically different from Smith's, they have similar overall structures to each other. The contribution of this paper is two-fold. First, based on the derivation of Smith, the authors point out that Grangeat's inversion formula and Smith's can be conveniently described using a single formula (the Smith-Grangeat inversion formula) that is in the form of space-variant filtering followed by cone-beam backprojection. Furthermore, the resulting formula is reformulated for data acquisition systems with a planar detector to obtain a new reconstruction algorithm. Second, the authors make two significant modifications to the new algorithm to reduce artifacts and numerical errors encountered in direct implementation of the new algorithm. As for exactness of the new algorithm, the following fact can be stated. The algorithm based on Grangeat's intermediate function is exact for any complete orbit, whereas that based on Smith's intermediate function should be considered as an approximate inverse excepting the special case where almost every plane in 3-D space meets the orbit. The validity of the new algorithm is demonstrated by simulation studies

[en] Noise equivalent counts are a convenient and effective means to assess PET emission image quality. The authors have extended the method to include the effects of transmission imaging on the statistics of attenuation corrected PET data. The result of the calculations is a noise figure which describes the SNR performance of the elements of the attenuation corrected emission sinogram. The noise figure demonstrates the tradeoff between emission and transmission imaging performance, and can be used to determine optimal partitioning of imaging time between emission and transmission scans. Also, the technique can be used to compare the efficacy of simultaneous transmission/emission imaging techniques and multiple orbiting rod source geometries. Experimental and simulated results from the GE 2,048 PET scanner are used to demonstrate the model. In a sample imaging situation in that system geometry [0.2 μCi/cc activity in a 20-cm flood phantom, 3-mCi orbiting rod source(s)], the dual rod source achieves 80 percent of the noise figure improvement which is available in simultaneous transmission/emission imaging without transmission data filtering, and demonstrates superior performance when a 3-point averaging transmission filter is applied