Friday 10:30-12:00, Pier IV & V & Lobby

Chair: Mark F. Smith, National Institutes of Health

C. Michel¹, M. Sibomana¹, A. Bol¹, X. Bernard¹, M. Defrise², C. Comtat³, P.E. Kinahan³, D.W. Townsend³

^{1PET Laboratory, Catholic Univ. of Louvain, Louvain-la-Neuve, Belgium, 2Division of Nuclear Medicine, Free Univ. of Brussels AZ-VUB, Brussels, Belgium, 3Dept. of Radiology, Univ. of Pittsburgh, Pittsburgh, USA}

In order to preserve the Poisson characteristics of PET data when using OSEM iterative reconstruction, we have first modified the attenuation weigthing scheme to include normalization as a global multiplicative weight. In a second step, we have completed the weighting scheme by considering random coincidences and Compton scatter as global additive noise. The two new schemes have been implemented and tested using 2D dynamic data from a decaying phantom filled with H2O15. The OSEM images produced by four weighting schemes: unweighted, attenuation, attenuation and normalization, and fully weighted were compared to the ones obtained with the filtered backprojection (FBKP) used as a reference. Any bias was hard to observe from our phantom data. The impact of the reconstruction methods on physiological parameters is illustrated with a clinical protocol measuring cardiac blood flow at rest.

A. Raheja¹, A.P. Dhawan¹

^{1Dept. of BioEngineering, Univ. of Toledo, Toledo, OH}

Maximum Likelihood estimation based Expectation Maximization(EM) reconstruction algorithm has been shown to provide good quality reconstruction for PET. This conventional EM algorithm suffers from slow convergence and results in noisy images. The multiresolution EM algorithm is an attempt to improve the EM based estimation through an effective use of multi-resolution grids in both image- reconstruction and detector spaces. The detectors in the PET ring are combined i.e. the tube data is rebinned to result in multi-resolution detector space. The algorithm begins iterating with the coarsest grid level in both spaces and switches both image and detector grid levels simultaneously until the finest detector and image grid level are reached. This algorithm incorporates a wavelet decomposition based transition criterion for switching grid levels and a wavelet spline based interpolation method for projecting the intermediate reconstruction from a specific image grid level to the next finer grid.

T. Cao-Huu^1,2, G. Lachiver², C. Burnham³, D. Kauffman³, G. Brownell^3,4, J. Correia³

^{1Harvard Univ., 2Universite de Sherbrooke, 3Massachusetts General Hospital, 4MIT}

The system matrix, A, arising from the natural pixel basis representation is full, rank-deficient, and very large. Solution of this large system of equations presents significant difficulties. Krylov-subspace based algorithms were proposed and developed to overcome these limitations. It follows that the application of two regularization techniques, the Truncated Singular Value Decomposition (SVD) and the Tikhonov-Phillips method are necessary in order to obtain stable and reliable solutions. Examples are demonstrated with noisy data from the micro-PET imager being built at MGH by Correia et al.

H.A. Kudrolli¹, W.A. Worstell¹, V.G. Zavarzin¹

^{1Boston Univ. Physics Dept.}

Abstract-- We have developed a 3D PET reconstruction algorithm based upon Inverse Monte Carlo analysis, and have tested it on data acquired by high-resolution 3D PET detectors. Our algorithm back-projects 3D PET data across a 3-dimensional array of voxels, then during each iteration generates Monte Carlo pseudo-data which is similarly back-projected across a 3-dimensional voxel array. Comparison between the back-projection of the data and the back-projection of the pseudo-data is used to update the source distribution hypothesis used as input for the pseudo-data generation. Inverse Monte Carlo methods provide a natural framework for incorporation of detector response functions, and potentially for the incorporation of effects due to scatter and other sources of systematic error. The algorithm is fairly fast, capable of reconstructing a 128 x 128 x 128 Hoffman brain phantom image in a few hours on a modern single-processor workstation. The algorithm is also readily parallelized, and we have achieved nearly linear speed-up with a simple implementation on a 16-processor array.

S. Huang¹

^{1Division of Nuclear Medicine and Biophysics, Dept. of Molecular and Medical Pharmacology UCLA School of Medicine, and Laboratory of Structural Biology and Molecular Medicine}

OS-EM can accelerate the convergence speed of EM reconstruction, but intermediary images oscillate over sub-iterations. We have investigated two approaches, sinogram preprocessing and subiteration smoothing, to reduce the oscillation problem with the goal of accelerating further the convergence. Computer simulation and real PET scans were used to evaluate the approaches. Simulated sinograms were generated from Hoffman's phantom with various noise levels. Standard OS-EM was first applied to reconstruct the images. The reconstruction was repeated with the new approaches incorporated. Image values on selected ROIs were obtained over subiterations and compared with those by the standard OS-EM reconstruction. Results show that both approaches are effective in reducing the oscillations over sub-iterations. Oscillation of ROI values was reduced by a factor of more than 2.5 (in S.D.) with the new approaches. Images obtained with the new approaches have lower noise levels (1/2 to 1/3) than with the standard OS-EM of same number of iterations.

H. Urabe¹, K. Ogawa¹

^{1Hosei Univ., Tokyo, Japan}

In ordered subsets- expectation maximization (OS-EM) the projection data are grouped into subsets of projection data. The method can also be applied to the maximum a posteriori (MAP) method. We call it OS - Bayesian Reconstruction (BR) method. The aim of the study is to improve the reconstructed image by the OS-BR method. Generally, the ordered subset algorithm uses a fixed number of projections, so called ``subset levels''. The recovered frequency-component of a reconstructed image depends upon the number of projections in a subset. We propose a new method named MOS (Modified OS)-BR which modifies the number of projections for each iteration step in an OS-BR algorithm. We compared the MAP-EM, OS-BR and MOS-BR. From the results in all of the examples the mean absolute error were decreased stably with MOS-BR and the proposed method was extremely effective when the projection data included a lot of noise.

G. Kontaxakis¹, L.G. Strauss¹, G. van Kaick¹

^{1German Cancer Research Center (DKFZ), Division of Oncological Diagnostics and Therapy, Im Neuenheimer Feld 280, Heidelberg , Germany}

The ordered subsets technique applied for the acceleration of the maximum likelihood expectation maximization iterative image reconstruction (IIR) algorithm for emission tomography, is here extended to several other IIR methods, namely the weighted-least squares, image space reconstruction algorithm and the maximum likelihood space alternating generalized EM. Additional acceleration is expected with the use of the successive substitutions method. The median root prior has been successfully applied to control the noise level in the reconstructed images with increasing iteration numbers. All methods are implemented on distributed Pentium systems and a Javascript is used for the initiation of the reconstruction of a selected study. An efficient implementation for dynamic multi-tracer PET studies allows the reconstruction of one frame in a few minutes on Pentium systems. The development and optimal combination and parameter selection for these IIR techniques will be presented, along with results on their performance on patient data from the ECAT EXACT HR+ scanner.

P.R. Marechal^1,2, D. Togane², A. Celler², J.M. Borwein¹

^{1CECM-Dept. of Mathematics and Statistics, Simon Fraser Univ., Burnaby BC, Canada, 2Div. of Nuclear Medicine, Vancouver Hospital and Health Sci. Centre, Vancouver BC, Canada}

Tomographic image reconstruction has been extensively studied, but comparison of the performance of reconstruction methods remains an open problem. The goal of this work is to demonstrate how concepts from applied mathematics can provide useful information on the stability and fidelity of standard FBP as well as entropy based methods. The stability of a method is assessed from the spectral norm of the sensitivity matrix; the fidelity corresponds to the difference of the experimental and reconstructed image projection data. We have studied this approach using simulations and standard FBP with various filters and confirmed the expected conflict between fidelity and stability for FBP (low cutoffs improve stability but degrade fidelity). These techniques are now being applied to entropy-like methods. This analysis provides quantitative information that could allow the informed selection of reconstruction parameters and techniques. Also, the interpretation of reconstructed images will benefit from quantitative information about the reconstruction error.

S.S. Gleason¹, S.J. Norton¹, H. Sari-Sarraf¹, M.J. Paulus¹, D.K. Johnson¹

^{1ORNL, Oak Ridge, TN}

Traditional (filtered backprojection, or FBP) and statistical (e.g., maximum likelihood) tomographic image reconstruction techniques have been applied to sinogram data generated by a new X-ray computed tomography system under development at the Oak Ridge National Laboratory. This unique system is being developed to image laboratory mice for the purpose of phenotype screening and identification. This CT system allows simultaneous capture of several sets of sinogram data, each having a unique X-ray energy distribution, or bin. Due to varying numbers of photon counts within each energy bin, both FBP as well as maximum likelihood techniques were applied to the energy-dependent sinogram data. Comparisons of reconstructed images using both algorithms on multi-energy (both high- and low- count) sinogram data are presented.

E.T. Slijpen¹, F.J. Beekman¹

^{1Dept. of Nuclear Medicine, Univ. Hospital Utrecht}

Iterative reconstruction of Single Photon Emission Computed Tomography (SPECT) images requires regularization to avoid noise amplification and edge artifacts at high iteration numbers. This paper compares optimal post smoothing (OPS) after iterative reconstruction with iterative reconstruction using optimal smoothing in between (OIS) each iteration step. The reconstruction algorithm used was Ordered Subset Expectation Maximization (OS-EM). A fast SPECT simulator is used to generate training sets consisting of phantoms and corresponding SPECT images. The filters are restricted to 3D isotropic Gaussians. The optimal filters are selected by varying the width of the kernel till the difference defined between the distribution of a brain phantom and its corresponding filtered SPECT image is minimized. It is shown that the difference between OPS and OIS images is extremely small. When training sets are available, OPS is much easier and faster optimized then OIS.

R.G. Wells¹, P. Simkin¹, P.F. Judy², M.A. King¹, P.H. Pretorius¹, H.C. Gifford¹, P. Schneider¹

^{1Univ. of Massachusetts Medical Center, Worcester, MA, 2Brigham and Women's Hospital, Boston, MA}

Iterative reconstruction algorithms are usually halted after a specific number of iterations or are regularized using priors or a penalty function. It is difficult to know a priori what is the optimal combination of regularization methods. One method of selection is to use a localization receiver operating characteristic (LROC) study. LROC uses a more clinical task and provides more statistical power than ROC. Using LROC, we are investigating the combination of iteration number and 3D Gaussian filter which will maximize the detectability and localization accuracy of 1cm gallium-avid tumors in OSEM SPECT reconstructions of the chest region. In our study, each of the five observers used reads 200 images per test condition, divided equally over two reading sessions. In each case, the observer indicates the most probable location of the lesion in the image and provides a confidence rating (as in an ROC experiment). Our preliminary results indicate a preference towards low iteration number (<=2 iterations of OSEM) and moderate smoothing (a 2-4 pixel FWHM filter).

C.I. Amblard¹, P.E. Grangeat¹, H.E. Benali², B.E. Bendriem³

^{1LETI, DSYS, CEA-G, Grenoble, france, 2ISERM u66, Paris, France, 3SHFJ, CEA, France}

Point-source reconstruction arises as a main issue in a large class of applications. Metastasis detection or cerebral activation studies from PET or SPECT data, restoration of astronomic data, radioactivity sources detection in nuclear waste control or nuclear installation dismantlment are some examples. In this paper, we present a general point source reconstruction method and we describe its application to hyperfixation point-source reconstruction in PET for oncology.

In the second part, we point out the inherent difficulties of this issue and the limits of classical methods to solve them. The third part introduces statistical framework of the Maximum Entropy on the Mean method. Selecting a solution based on realistic statistical model without introducing spatial smoothing operation, this method seems relevant to solve underdeterminated problem. The fourth part deals with the application of the method to hyperfixation point-source reconstruction in PET for oncology.

V. Selivanov¹, Y. Picard¹, J. Cadorette¹, S. Rodrigue¹, R. Lecomte¹

^{1Metabolic and Functional Imaging Center, Université de Sherbrooke}

One limitation in practical implementation of iterative reconstruction is to build a transition matrix accurately modeling the relationship between projection and image spaces. Detector response functions (DRF) in PET are broad and spatially-variant, leading to large transition matrices taking too much space to store. In this work, we investigate the effect of simpler DRF models on image quality in ML-EM reconstruction. We studied 6 cases of increasing complexity: simple tube/pixel geometric overlap; geometric overlap with tubes centered on DRF maximum; fixed-width Gaussian centered on DRF maximum; same as previous with Gaussian of same spectral resolution as DRF; same with Gaussian aligned on median of DRF; f) simulated DRF based on linear attenuation of &#61543;-rays in detector arrays. Oversimplification of DRFs may affect image quality dramatically. However, simulated DRFs generate a transition matrix that can be easily fitted into the memory of current stand-alone computers and yield images of excellent quality for a small animal PET system with long, narrow detectors.

W. Wang¹, B.M. Tsui^1,2, E.C. Frey^1,2, D.E. Wessell¹

^{1The Univ. of North Carolina at Chapel Hill, Dept. of Biomedical Eng., 2The Univ. of North Carolina at Chapel Hill, Dept. of Radiology}

This study compares two collimator-detector response (CDR) compensation methods in SPECT, an analytical method by Pa n et al. and an iterative method which uses the OS-EM algorithm. The spatial resolution recovery was evaluated using simulated data of a point source placed at different distances from the center of rotation. The image noise propert ies were evaluated using simulated data from a uniform disk phantom. The two methods provide general improvement in resolution but generate reconstructed point source images showing different asymmetric shapes. The analytical method is fast but assumes CDR characteristics that are not fully met in practice. It amplifies high frequency noise drast ically. To reduce the noise level, a smoothing filter is used with concurrent degradation in resolution. The it erative method is slower but accurately models the CDR function with lower noise in the reconstructed images. The iterative method provides more accurate CDR compensation and lower image noise as compared to the a nalytical method at a cost of longer computation time.

C. Kao¹, X. Pan¹, M.A. Anastasio¹, P. La Riviere¹

^{1Univ. of Chicago}

In this work, we develop a DFT-based method for the interpolation of a real sequence that does not necessarily satisfy the Shannon-Whittaker sampling condition. The proposed approach is based on the idea of signal recovery such that the interpolation solution is the sequence of the desired length that minimizes a cost function and passes through the original sampled points. The cost function is designed so that the solution obtained is a tradeoff between the smothness and the resemblance to a prototype solution. In addition to FFT, all computations involved are simple arithmetical operations; consequently, the proposed method is computationally efficient. Our primilinary computer experiments demonstrate that the proposed method can produce good interpolation results even when the functions are undersampled.

X. Pan¹

^{1The Univ. of Chicago}

We have shown previously that two estimates of the Fourier transform (FT) of the ideal sinogram of an image can be obtained from the measured data in 2D SPECT with uniform attenuation. We have proposed also taking a linear combination of the two estimates for reduction of the global variance in the reconstructed image. In this work, we show that the use of a complex combination coefficient for the linear combination of the two estimates can, in principle, provide a smaller global image variance than does the use of a real combination coefficient. However, we demonstrate semi-analytically as well as numerically that it is practically impossible to choose an adequate non-zero imaginary part of this complex combination coefficient to achieve the theoretical predictions. Instead, in practice, so that amplification of data noise is prevented, only a real combination coefficient should be used for obtaining the final estimate of the ideal sinogram. These claims have also been validated quantitatively by our extensive numerical simulation studies.

J. You¹, J. Li¹, Z. Liang¹

^{1Dept. of Radiology, SUNY, Stony Brook, NY -8460}

The low spatial resolution of SPECT image is mainly due to the limited collimator resolution. This is because collimator hole diameters must be relatively large to obtain reasonable efficiencies and the source-to-detector distance generates much blurring of the image. Lewitt et al developed an approximate correction algorithm to restore the depth-dependent collimator blurring by the Fourier decomposition of sinogram. In this work, when the collimator response is represented as a fan-region integral of the radionuclide distribution, an accurate restoration procedure is investigated for such projection data.

A.R. Formiconi¹, A. Passeri¹, P. Calvini²

^{1Univ. of Florence, 2Univ. of Genova}

A theoretical formulation of the geometric transfer function of multihole collimators which provides both efficiency and spatial resolution information in the same formula is presented. The formulation is used for modeling the point spread function (PSF) of the collimator in SPECT reconstruction algorithms. The agreement between experimental data obtained with line sources and the theoretical predictions is good and the discrepancies do not exceed the experimental errors. Lookup tables of weighting factors to be used in iterative reconstruction algorithms are calculated and compared with those obtained from experimental procedures for various collimators. Patients brain SPECT studies reconstructed both with the theoretical and experimental lookup tables are also compared.

C. Tocharoenchai¹, B.M. Tsui¹, D.P. Lewis¹, E.C. Frey¹, X. Zhao¹

^{1Univ. of North Carolina at Chapel Hill}

This study is to improve Ga-67 static and SPECT images by compensating for the response function of a medium energy (ME) collimator. The point response functions (prf) of the ME collima tor for the 93, 185 and 300 keV photons at 5, 10, 15 and 20 cm from the collimator face were determined using a Ga-67 point source. They show hole patterns at all and increased penetrat ion at higher photon energies. To evaluate the compensation methods, static images and SPECT projection data were acquired from a phantom con sisting of 3 hot spheres with diameters of 1, 1.3 and 1.6 cm inside a cylindrical phantom. The hole pattern is seen in the phantom data at small pixel sizes. From the prf's, Butterworth filters were designed that reduce the hole pattern without degrading the overall resolution. An iterative OS-EM reconstruction method that incorporates the distance varying prf provides SPECT images with improved resolution and less artifacts than that in FBP reconstructed images. We conclude that degradation caused by ME collimator in Ga-67 imaging can be effectively compensated.

H. Kudo¹, F. Noo², M. Defrise³

^{1Inst. of Information Sci. and Electronics, Univ. of Tsukuba, Japan, 2Univ. of Liege, Belgium, 3Free Univ. of Brussels, Belgium}

This paper is concerned with reconstruction of axially truncated cone-beam projections. This problem is of great importance for future developments of x-ray CT. First, we generalize Grangeat's formula such that multiple cone-beam projections, which provide a kind of triangulation of a plane, are combined to calculate each 3-D Radon transform in a mathematically rigorous way. The final result shows that the previous similar formulations by Tam and Kudo and Saito need to consider an additional term called the boundary term. Furthermore, this result leads to a two-step reconstruction algorithm (RADON algorithm) which can be considered a generalization of Gramgeat's algorithm. Second, the RADON algorithm is reformulated to obtain a filtered backprojection (FBP) style algorithm (CB-FBP algorithm) for the truncated cone-beam projections. We implemented both the RADON and CB-FBP algorithms for the helical vertex path. The results show that the new algorithms are more accurate than the conventional Feldkamp algorithm.

A.V. Bronnikov¹

^{1KEMA Nederland B.V.,}

We present a new approach to 3D image reconstruction, extending cone-beam reconstruction theory to inversion of the exponential cone-beam transform, which may serve as a mathematical model in 3D SPECT brain imaging. Our method requires two computation steps: backprojection and filtering. The latter is implemented in the frequency domain. Unlike the Tretiak-Metz filter, our filter has no low-frequency cutoff, enabling rigorous implementation and providing better noise properties. To ensure shift-invariancy, we resort to an approximation, assuming that the detector has a large focal length. Limitations of this approximation are investigated in numerical experiments. Satisfactory results were obtained using detectors with relatively short focal lengths.

H. Hu¹

^{1General Electric Company}

Multi-slice CT system refers to the special CT system that is equipped with a detector array of multiple rows to simultaneously acquire data at different z locations. Multi-slice CT represents a major improvement in CT performance. In this paper, we investigate an unique characteristic in multi-slice helical CT acquisition, i.e., the existence of the optimal helical scan pitch. We discuss the preferred helical pitches of 4 slice CT scanner. We present the helical reconstruction algorithms for multi-slice CT in general and for 4-slice CT in particular. The multi-slice CT reconstruction proposed contains a z resolution parameter in reconstruction to further vary the tradeoff of the slice thickness versus image noise and artifacts. We also evaluate the performances of a 4-slice CT scanner.

The results of simulation and experiment as well as initial patient studies proved that with the design proposed, the 4-slice helical CT can provide equivalent image quality with improved z-axis resolution at twice of the table speed and at 1/2 of the mA of the single slice helical CT.

H. Turbell¹, P. Danielsson¹

^{1Image Processing Laboratory, Dept. of Electrical Eng., Linkoping Univ., 581 83 Linkoping, Sweden}

We have invented and implemented a new method for 3D-reconstruction of long objects. Data are captured in a 2D-detector window, which covers the full object cylinder width, but is limited in the other direction by two consecutive turns of the helix. This detector arrangement ensures complete and non-redundant data capture, where each object point is exposed during a source rotation of of 180 degrees as seen from the point itself. This detector window has been used in the past for exact reconstruction. Our reconstruction algorithm is non-exact and employs only one-dimensional filtering. The first step is rebinning to parallel projections as seen along the axis of the helix cylinder. This rebinning maps the detector window and the projections onto a perfectly rectangular virtual detector plane. The remaining step consists of nothing but 1D-ramp-filtering in this detector plane followed by ordinary backprojection. We claim that the image quality is equal or superior to images produced by previous non-exact algorithms while the detector size and data capture is minimized.