Friday 1:30- 3:00, Pier IV & V & Lobby

Chair: David S. Lalush, The University of North Carolina at Chapel Hill

K. Lauckner¹, W. Enghardt¹, R. Hinz¹, J. Pawelke¹

^{1Forschungszentrum Rossendorf, Postfach 510119, D- Dresden, Germany}

A specially built PET-system BASTEI (Beta Activity meaSurements at the Therapy with Energetic Ions) has been integrated into the heavy ion tumour therapy facility at the Gesellschaft fr Schwerionenforschung (GSI) in Darmstadt in order to monitor and control the applied dose distribution. This paper presents a fully 3D image reconstruction method based on the MLEM algorithm adapted to BASTEI and the results of performance studies. BASTEI has a strongly spatially-varying system behaviour due to its limited angle design and the presence of detector gaps. Furthermore, the expected image quality is limited by the low counting statistics. Corrections for attenuation, outside activity, parallax errors, randoms as well as nomalization factors have been implemented. The algorithm has been validated with 22Na reference sources and in realistic studies, where phantoms have been irradiated with 12C beams. Resolution, edge detectability, geometrical fidelity of size and position were chosen as figures of merit. Since December 1997 it has been applied successfully to patient data.

K.E. Timmermann¹, R.D. Nowak¹

^{1Michigan State Univ.,}

It is well-known that the noise in single photon emission computed tomography (SPECT) obeys a Poisson distribution and, therefore, is signal-dependent. Consequently, spatially-adaptive filtering is required for optimal noise removal. In this paper we extend a wavelet-based modeling and estimation approach previously developed by the authors in timmermann1 for general Poisson processes, and apply it to the SPECT problem. We develop practical prior models for the sinogram image, which we use to optimally remove noise from the projection data prior to reconstruction. The impact of the new filtering approach on SPECT imaging is illustrated through simulation and with clinical data.

M.I. Krzywinski¹, V. Sossi¹, T.J. Ruth¹

^{1TRIUMF/Univ. of British Columbia}

We have evaluated the performance of FORE+2DFBP, FORE+OSEM and FORE+SAGE on 3D PET data and compared reconstructions to the current 3DFBP standard. We have found that FORE+2DFBP offers 20% better axial uniformity and is identical compared to 3DFBP with respect to resolution, noise, contrast recovery, and SNR. Logan analysis of patient data using cortical and cerebellar input functions gave results consistent with no difference between 3DFBP and FORE+2DFBP (0.060.59% difference for cortical input and -1.92.2% for cerebellar input). We conclude that 3DFBP can be replaced with FORE+2DFBP, offering a 8-fold decrease in reconstruction time. FORE+OSEM behaved optimally compared to 3DFBP with 12 subsets and 4 iterations with a 4 Gaussian mm filter and is 5 times faster then 3DFBP. FORE+SAGE behaved best for log2b=-5 and convergence was reached after 10 iterations and 3 times faster than 3DFBP. Both methods offer higher resolution at the same noise level as 3DFBP and yield better axial uniformity but show a systematic difference in Logan DVR of as much as 4%.

K. Mueller^1,2, R. Yagel^1,2

^{1Dept. of Computer and Information Sci., The Ohio State Univ., Columbus, OH, USA, 2Biomedicom Ltd., Jerusalem, Israel}

The Algebraic Reconstruction Technique (ART) has many advantages over Filtered Backprojection approaches, and has also recently been shown to perform well for 3D cone-beam reconstruction. However, ART's slow speed has prohibited its routine use in clinical applications. In this paper, we devise a hardware assisted acceleration scheme, employing readily available texture mapping graphics hardware, that performs a quality parallel-beam and cone-beam reconstruction at almost interactive speeds.

S. Vollmar¹, W. Eschner², U.K. Pietrzyk^1,3

^{1MPI fuer neurologische Forschung, Koeln, Germany, 2Klinik und Poliklinik fuer Nuklearmedizin, Universitaet zu Koeln , 3Bergische Universitaet Gesamthochschule Wuppertal, Fachbereich Physik}

Our aim was to enhance resolution and signal to noise ratio of PET reconstructions by incorporating information of other image modal- ities (MRT, CT) into the reconstruction process. We combined a fast iterative method with a method for reconstruction with a-priori-in- formation that is based on the ML-EM reconstruction and makes use of Bayes rule and Markov random fields. In our model, a potential function with a parameter beta determines the influence of the a-priori- information on the reconstruction process. The main problem with incorporating a-priori-information into the reconstruction process is to find a compromise between making insufficient use of the seg- mentation of MRT or CT data on the one hand and a reproduction of the a-priori-information on the other hand. We examined the influence of incorrect a-priori-information using computer generated and experimental data. Our results show that intervals of the a-priori-parameter beta can be found in which our method is robust regarding incorrect a-priori- information.

V.Y. Panin¹, R.E. Basko¹, G.L. Zeng¹, G.T. Gullberg¹

^{1Dept. of Radiology, Univ. of Utah}

An iterative Bayesian reconstruction algorithm based on the total variation (TV) norm constraint is proposed. The motivation for using TV regularization is that it is effective for recovering edges of images. The TV norm minimization, introduced in 1992 was shown to be effective for restoring blurred images with a Gaussian noise model and was demonstrated to be effective for noise suppression and edge preservation. The images were diffused according to a set of nonlinear anisotropic diffusion partial differential equations, which suffered from computational difficulties. This paper extends the TV norm minimization constraint to the field of SPECT image reconstruction with a Poisson noise model. The regularization norm is included in the ML-EM algorithm. The partial differential equation approach is not utilized here. Reconstructions of computer simulations and patient data show that the proposed algorithm has the capacity to smooth the noise and maintain sharp edges without introducing over/under shoots and ripples around the edges.

J.S. Maltz^1,2, E. Polak², T.F. Budinger^1,2

^{1Center for Function Imaging, LBNL, 2Dept. of Electrical Eng. and Computer Sci., Univ. of California, Berkeley}

We present a hybrid multistart algorithm for the joint optimisation of spatial and kinetic parameters in dynamic ECT, where maximisation of the least squares cost function is performed in projection space. Simulated annealing is employed to sample the parameter domain on a coarse grid. Potential solutions are then refined using a stabilised Newton algorithm with an Armijo line search. The performance of the algorithm in fitting a multiple ellipse region model to a dynamic projection set is evaluated at varying noise levels. We present experimental results which verify that a global search is required to avoid convergence to sub-optimal local minima, and that the scale invariant property of Newton's method enables convergence to an optimum in regions where the behaviour of the gradient function leads other optimisation methods not endowed with this property to fail.

Y.I. Picard¹, V. Selivanov¹, M. Verreault¹, R. Lecomte¹

^{1Dept. of Nuclear Medicine and Radiobiology, Universite de Sherbrooke}

The ML-EM reconstruction algorithm is an iterative computation of tomographic images by maximisation of a likelihood function of the Poisson emission rates. The method being time consuming, a parallel version can easily be implemented to distribute the reconstruction task on multiple processors. Since general purpose supercomputers are costly and their parallel programming are platform-dependent, distributed ML-EM processing on a network of workstations is an attractive alternative. However, communications of the computed partial projections among nodes are time consuming on typical networks such that there is a relatively low limit on the number of processors which can participate in the computation and still reduce reconstruction time. Optimizing the communication process by using efficient hardware and message passing interface, and by transferring sums of partial projections instead of the partial projections themselves over the network permits the distribution of the reconstruction task over a larger number of nodes while reducing the overall reconstruction time.

P. Sukovic¹, N.H. Clinthorne¹

^{1The Univ. of Michigan}

In this paper results of dual energy reconstructions in X-ray tomography are presented. Simultaneously obtained X-ray scans and emission tomography scans can be combined to create combined anatomical-functional images. Moreover, emission attenuation coefficients can be estimated from X-ray attenuation coefficients. As low fluxes as possible should be used, than, and the implementation of iterative algorithms becomes desirable. Dual energy reconstruction algorithm utilizing penalized least squares objective function was used. Uncertainty was estimated directly from the projections. The method was compared to the non-data weighted case corresponding to direct reconstruction methods. In low attenuation case both algorithms showed the similar performance. However performance of the data-weighted algorithm was improved over the performance of the non-data weighted algorithm in all regions, except in soft tissue - bone contact region. The streaks are probably due to the poor estimate of uncertainty in highly attenuated rays. Ways to account for this effect are currently being investigated.

A. Rangarajan¹, I. Hsiao², G.R. Gindi²

^{1Departments of Diagnostic Radiology and Electrical Eng., Yale Univ., 2Departments of Radiology and Electrical Eng., SUNY Stony Brook}

In brain SPECT (and PET), various schemes to aid the SPECT reconstruction with MR side information have been proposed. Many of these amount to controlling smoothing within anatomical regions but not across regions. Here we propose a different approach based upon the mutual information of SPECT and MR. The basic idea is to perform SPECT reconstruction while maximizing the mutual information between the evolving SPECT reconstruction and a co-registered MR scan. Note that mutual information is not being used as metric for MR-SPECT registration. Given K MR clusters and L SPECT clusters, the KxL clusters in the histogram are fitted by a mixture of gammas that is used as a prior. We demonstrate that this scheme remains effective when the number of SPECT classes (e.g. gray, white, csf, hotspot hence L=4) is unequal to the number of MR classes (gray white csf hence K = 3). The entire procedure may be cast as the MAP (maximum a posteriori) solution to a Bayesian problem.

S. Lee¹, Y. Choi², G.R. Gindi³

^{1Dept. of Electronic Eng., Paichai Univ., Taejon, Korea., 2Dept. of Nuclear Medicine, Samsung Medical Center, Seoul, Korea, 3Dept. of Radiology, SUNY at Stony Brook, Stony Brook, NY}

The variety of Bayesian MAP approaches proposed in recent years can both stabilize the reconstructions and lead to better bias and variance. In our previous work, we showed that the thin-plate (TP) prior, which is less sensitive to variations in first spatial derivatives than the conventional membrane (MM) prior, yields improved reconstructions in the sense of low bias. In spite of this advantage, however, the TP prior often exhibits overshoots around discontinuities. In contrast, the MM prior tends to oversmooth the discontinuities. In order to reduce these drawbacks in each model, we generalized the prior energy to a convex combination of MM and TP using a control parameter, and observed its transition between MM and TP. In this work, we used physically acquired data to validate the effects of the new prior models by modeling a PET scanner. For more accurate attenuation correction, we used a Bayesian approach to reconstruct attenuation maps. Our results show that the solution obtained with the hybrid model reduces overshoots in TP as well as oversmoothness in MM.

V.Y. Panin¹, G.L. Zeng¹, G.T. Gullberg¹

^{1Radiology, Univ. of Utah}

Previously we developed algorithms to obtain transmission reconstructions from truncated projections and from emission data without transmission measurements. The optimal basis set or "knowledge set" was used to create an approximate attenuation map, and the expansion coefficients were estimated using reconstruction algorithms. Since a truncated expansion does not represent an image precisely, and the projections of the basis vectors are not orthogonal, the estimated coefficients can be unstable in the presence of systematic error. A constraint, based on distribution of the expansion coefficient, is considered in this paper to regularize the estimation problem. The parameter selection methods based on different assumptions are applied to find the optimal regularization parameter. The selected regularization parameter obtained from a projection data set has been shown to provide satisfactory reconstruction results.

C. Kao¹, X. Pan¹

^{1Univ. of Chicago}

We have developed previously infinite classes of closed-form methods for image reconstruction in 3D SPECT with uniform attenuation and distance-dependent spatial resolution. In this work, we implemented these closed-form methods for fast and accurate reconstruction of 3D SPECT images. Using these implemented methods, we studied systematically and quantitatively the effects of 3D distance-dependent blurring, attenuation, and various approximations that are introduced in the process of development of these closed-form methods on the reconstructed images. Our implemented methods require less than two minutes to reconstruct a 128X128X128 SPECT image from a data set of sizes of 128X128X128 on a modern low-end personal computer. Because our developed computer programs for these 3D closed-form methods are extremely fast computationally, we are able to investigate the noise properties in the reconstructed images empirically from a large number (~3000) of reconstructed 3D images by using computer simulated noisy data.

X. Liu¹, M. Defrise¹, C. Michel², M. Sibomana², C. Comtat³, P.E. Kinahan³, D.W. Townsend³

^{1Division of Nuclear Medicine, Vrije Universiteit Brussel, Belgium, 2PET Laboratory, Universite Catholique de Louvain, Belgium, 3PET Facility, Univ. of Pittsburgh, Pennsylvania}

The standard way to reconstruct 3D PET data is the reprojection algorithm (3DRP). The need for faster reconstruction has led to the development of approximate methods such as the Fourier rebinning (FORE) algorithm, which reduce 3D data to a 2D data set. The accuracy of FORE might not be sufficient for future scanners with large axial aperture. We describe two methods based on an exact rebinning formula. The first one is a fast forward projection algorithm which can be used to calculate 3D attenuation correction factors from 2D transmission data. The second one is a 3D reconstruction algorithm, FOREX, which is faster than 3DRP. The algorithm has been applied to a 3D brain scan acquired with an ECAT HR (CTI/Siemens) and also to data simulated for a scanner with a 30 deg. aperture. No significant difference between FORE and FOREX is observed for the real data, but the exact rebinning is more accurate than FORE for the simulated data. The main drawback of the exact rebinning methods is the large memory requirement.

P.J. La Riviere¹, X. Pan¹

^{1Dept. of Radiology, The Univ. of Chicago}

A number of methods exist specifically for the interpolation of periodic functions from a finite number of samples. In this work, we derive analytic expressions for the covariance and variance of the curves interpolated by three such methods--circular sampling theorem (CST), zero-padding (ZP), and periodic spline (PS) interpolation--when the samples are corrupted by additive, zero- mean noise. We perform empirical studies for the special cases of white and Poisson noise and find the results to be in agreement with the analytic derivations. For white noise we find that CST and ZP interpolation yield curves with constant variance that is equal to the variance in the measured samples when the number of such samples is odd, and slightly lower when the number is even. PS interpolation yields a reduced variance at interpolated points between the measured samples, with the minimum falling midway between such samples. Similar trends are observed for Poisson noise. The studies have implications for the interpolation tasks encountered in few- view tomography.

P.J. La Riviere¹, X. Pan¹, B.C. Penney¹

^{1Dept. of Radiology, The Univ. of Chicago}

We investigate spline-based smoothing and interpolation algorithms that enable filtered backprojection (FBP) to produce high-quality tomographic images from a smaller number of views than is normally used. We first perform an effective, adaptive 2D smoothing of the sinogram which exploits Fourier transforms to reduce the dimensionality of the smoothing problem. The smoothing itself is performed using smoothing splines with smoothing parameters determined automatically from the statistics of the data using the generalized cross-validation algorithm. We then interpolate additional angular views using interpolating splines. When certain angular sampling conditions are satisfied, the algorithms mitigate noise and star artifacts without introducing additional artifacts. The technique could potentially be used to reduce imaging time in cardiac SPECT by acquiring fewer views, thereby reducing degradation by motion artifacts.

J. Li¹, Z.E. Liang¹, J.E. Ye¹

^{1State Univ. of New York at Stony Brook}

This work investigated two inversions for correcting the depth-dependent resolution variation. The first one of Lewitt et al considers accurately the resolution kernel, but approximates the inversion formula. The second one of Van Elmbt et al derives accurately the formula, but approximates the kernel. We implemented both methods rigorously, therefore, the results reflect their performances. Accurate kernels were measured. Projections of the Hoffman brain phantom were simulated using the kernels (attenuation and noise were ignored, in order to study the effect of resolution variation only). Reconstruction of the first method recovered resolution better at the phantom periphery, consistent with the theory that the formula is approximated for far-field regions. The second one showed a better resolution recovery at the central area, consistent with the approach that the kernel is approximated for near-field regions. The second method is very sensitive to the approximation. The first one is robust and, therefore, is the choice for quantitative SPECT.

M.J. Persson¹, T. Schaumann¹, S.M. Dale¹, D.E. Bone¹

^{1Division of Medical Eng., Karolinska Inst., Sweden}

A mobile limited view angle tomographic gamma camera system, based on Ectomography, has been developed for acute perfusion studies. To improve system sensitivity for myocardial perfusion imaging, slant hole collimators with up to 4 segments have been used clinically. However, circular artifacts may occur, if data are truncated in the projection images. The aim of this study was to investigate the effects of these artifacts, and propose ways of artifact suppression by modifying the current reconstruction algorithm; filtered backprojection. To study artifact suppression, simulations were performed using a computerized phantom. Projection data were extrapolated into the truncated region, using various techniques. Reconstructions from the extrapolated data showed almost no circular artifacts. Artifact suppression was also achieved with data from an animal study. In conclusion, we have shown that simple extrapolation can effectively reduce data truncation artifacts when using simulated projection data. However, for clinical data, further investigation is required.

K.L. Matthews II¹, D.L. Gunter¹, C.E. Ordonez¹, R.S. Miyaoka², T.K. Lewellen²

^{1Rush-Presbyterian-St. Luke's Medical Center, 2Univ. of Washington}

Experimental measurement of the energy-dependent point-source response function (PSRF) is being used to model the imaging characteristics of a SPECT system. A goal of this model is developing a reconstruction method that utilizes energy spectral information. Another goal is providing a model PSRF for validating Monte Carlo simulations and testing other reconstruction algorithms. The experimental data has been fitted in two stages to produce a concise description of the system PSRF. The PSRF, as a function of energy and spatial location, is specified by 14 parameters, modeling the image of a point source that would be measured at that location. The PSRF of the SPECT system has been parameterized further by modeling each of the 14 parameters by analytic functions of energy and spatial location. In this way, the energy-dependent PSRF of the SPECT imaging system can be calculated at any spatial location and energy. This paper reports on the results of both the second stage of PSRF parameterization and the image reconstruction based on the first stage parameterization.

H. Kudo¹, N. Miyagi¹, T. Saito¹

^{1Inst. of Information Sci. and Electronics, Univ. of Tsukuba, Japan}

Existing exact cone-beam reconstruction algorithms are based on Grangeat's formula which links a cone-beam projection with the 3-D Radon transform. This paper proposes a completely new approach to exact cone-beam reconstruction. The new algorithm does not explicitly compute the 3-D Radon transform from which we expect a short computational time and an improvement of image quality. The new algorithm is based on two well-known tomographic concepts which are the Feldkamp reconstruction and the Fourier synthesis. The algorithm consists of three steps. The first step successfully divides the vertex path into K subpaths and apply the Felkdmap reconstruction to each subpath. The second step computes the Fourier transform of K subimages. The last step is to synthesize the Fourier transform of true image from the Fourier transforms of subimages and to take the inverse Fourier transform. The simulation results show that the new algorithm is more than two times faster than the existing algorithms and much improves image quality for typical vertex paths.

G.M. Besson¹

^{1General Electric Company}

CT scanners acquire data one projection at a time. The fan-beam algorithm requires an expensive backprojector pixel-dependent weight. Methods of simplifying the reconstruction include rebining to parallel projections, via two steps: azimuthal interpolation, leading to the fan-parallel geometry, with data unevenly spaced on radial lines through the origin of Radon space, and a subsequent axial interpolation. The azimuthal step can be replaced by data re-sorting or channel-dependent delays; this paper investigates an "Arcsin" algorithm to reconstruct directly from the fan-parallel data. Although it is shown that the algorithm cannot be exact, a "natural" approximation is described.The pre-, post-convolution weights, and the reconstruction filter, are derived analytically. Results show that image quality matches that of fan-beam reconstruction. The Arcsin method eliminates the resolution-compromising axial interpolation and the costly backprojection weight. An "Arcsin" detector design is proposed for direct parallel reconstruction from fan-beam data.

R. Basko¹, G.T. Gullberg¹, L.G. Zeng¹

^{1Dept. of Radiology, Univ. of Utah, Salt Lake City, Utah, USA}

Cone beam geometry has become popular in both SPECT and transmission computed tomography especially in imaging of relatively small organs. A direct image reconstruction technique developed by Grangeat is based on the relationship between cone-beam projections and the first derivative of the Radon transform. This paper describes this relationship using an expansion in spherical harmonics and develops a new method for calculating the first derivative of the Radon transform from the cone-beam projections. The algorithm works as follows: First, expansion in spherical harmonics is obtained for con-beam projections. Then, a simple transformation is applied to the corresponding expansion coefficients. Finally, the values of the first derivative of the Radon transform are calculated by evaluating the expansion with the transformed coefficients. Computer simulations verified that this approach combined with Radon inversion formula allows to achieve high quality image reconstruction.

C. Comtat¹, P.E. Kinahan¹, J.A. Fessler², T.E. Beyer¹, D.W. Townsend¹, M. Defrise³, C. Michel⁴

^{1Dept. of Radiology, Univ. of Pittsburgh, Pittsburgh, USA, 2Dept. of Electrical Eng. and Computer Sci., Univ. of Michigan, Ann Arbor, USA, 3Division of Nuclear Medicine, Vrije Universiteit Brussel, AZ-VUB, Brussels, Belgium, 4PET Laboratory, Université Catholique de Louvain, Louvain La Neuve, Belgium}

The diagnostic utility of whole-body PET is often limited by the high level of statistical noise in the images. An improvement in image quality can be obtained by incorporating correlated anatomical information during the reconstruction of the PET data. The combined PET/CT tomograph (the SoMatom-ART SMART scanner) allows the acquisition of accurately aligned PET and CT whole-body data. We present results of incorporating aligned anatomical information from the CT during the reconstruction of 3D whole-body PET data. We use the FORE+PWLS method for the reconstruction and a label model to incorporate anatomical information. Since in practice mismatches between anatomical and functional data are unavoidable, the labels are blurred to reflect the uncertainty associated with the anatomical information. Results show the advantage of using anatomical information when a blurred label model is used, even in the presence of mismatches between CT and PET data.