Results 1  10
of
108
ConjugateGradient Preconditioning Methods for ShiftVariant PET Image Reconstruction
 IEEE Tr. Im. Proc
, 2002
"... Gradientbased iterative methods often converge slowly for tomographic image reconstruction and image restoration problems, but can be accelerated by suitable preconditioners. Diagonal preconditioners offer some improvement in convergence rate, but do not incorporate the structure of the Hessian mat ..."
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Cited by 76 (31 self)
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Gradientbased iterative methods often converge slowly for tomographic image reconstruction and image restoration problems, but can be accelerated by suitable preconditioners. Diagonal preconditioners offer some improvement in convergence rate, but do not incorporate the structure of the Hessian matrices in imaging problems. Circulant preconditioners can provide remarkable acceleration for inverse problems that are approximately shiftinvariant, i.e. for those with approximately blockToeplitz or blockcirculant Hessians. However, in applications with nonuniform noise variance, such as arises from Poisson statistics in emission tomography and in quantumlimited optical imaging, the Hessian of the weighted leastsquares objective function is quite shiftvariant, and circulant preconditioners perform poorly. Additional shiftvariance is caused by edgepreserving regularization methods based on nonquadratic penalty functions. This paper describes new preconditioners that approximate more accurately the Hessian matrices of shiftvariant imaging problems. Compared to diagonal or circulant preconditioning, the new preconditioners lead to significantly faster convergence rates for the unconstrained conjugategradient (CG) iteration. We also propose a new efficient method for the linesearch step required by CG methods. Applications to positron emission tomography (PET) illustrate the method.
GroupedCoordinate Ascent Algorithms for PenalizedLikelihood Transmission Image Reconstruction
 IEEE Tr. Med. Im
, 1996
"... This paper presents a new class of algorithms for penalizedlikelihood reconstruction of attenuation maps from lowcount transmission scans. We derive the algorithms by applying to the transmission loglikelihood a version of the convexity technique developed by De Pierro for emission tomography. The ..."
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Cited by 68 (27 self)
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This paper presents a new class of algorithms for penalizedlikelihood reconstruction of attenuation maps from lowcount transmission scans. We derive the algorithms by applying to the transmission loglikelihood a version of the convexity technique developed by De Pierro for emission tomography. The new class includes the singlecoordinate ascent (SCA) algorithmand Lange's convex algorithm for transmission tomography as special cases. The new groupedcoordinate ascent (GCA) algorithms in the class overcome several limitations associated with previous algorithms. (1) Fewer exponentiations are required than in the transmission MLEM algorithm or in the SCA algorithm. (2) The algorithms intrinsically accommodate nonnegativity constraints, unlike many gradientbased methods. (3) The algorithms are easily parallelizable, unlike the SCA algorithm and perhaps linesearch algorithms. We show that the GCA algorithms converge faster than the SCA algorithm, even on conventional workstations. An ex...
Statistical Image Reconstruction Methods for RandomsPrecorrected PET Scans
 Med. Im. Anal
, 1998
"... PET measurements are usually precorrected for accidental coincidence events by realtime subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for accidental coincidences but destroys the Poisson statistics. We propose and analyze two new approximations to the ex ..."
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Cited by 35 (16 self)
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PET measurements are usually precorrected for accidental coincidence events by realtime subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for accidental coincidences but destroys the Poisson statistics. We propose and analyze two new approximations to the exact loglikelihood of the precorrected measurements, one based on a "shifted Poisson" model, the other based on saddlepoint approximations to the measurement probability mass function (pmf). The methods apply to both emission and transmission tomography; however in this paper we focus on transmission tomography. We compare the new models to conventional dataweighted least squares (WLS) and conventional maximum likelihood (based on the ordinary Poisson (OP) model) using simulations and analytic approximations. The results demonstrate that the proposed methods avoid the systematic bias of the WLS method, and lead to significantly lower variance than the conventional OP method. The saddlepoint method provides a more accurate approximation to the exact loglikelihood than the WLS, OP and shifted Poisson alternatives. However, the simpler shifted Poisson method yielded comparable biasvariance performance to the saddlepoint method in the simulations. The new methods offer improved image reconstruction in PET through more realistic statistical modeling, yet with negligible increase in computation over the conventional OP method.
Overview of methods for image reconstruction from projections in emission computed tomography
 PROC. IEEE
, 2003
"... 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 t ..."
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Cited by 27 (2 self)
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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 singlephoton 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 threedimensional case to the twodimensional 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.
Stochastic Approximation and RateDistortion Analysis for Robust Structure and Motion Estimation
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2003
"... Recent research on structure and motion recovery has focused on issues related to sensitivity and robustness of existing techniques. One possible reason is that in practical applications, the underlying assumptions made by existing algorithms are often violated. In this paper, we propose a framework ..."
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Cited by 25 (13 self)
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Recent research on structure and motion recovery has focused on issues related to sensitivity and robustness of existing techniques. One possible reason is that in practical applications, the underlying assumptions made by existing algorithms are often violated. In this paper, we propose a framework for 3D reconstruction from short monocular video sequences taking into account the statistical errors in reconstruction algorithms. Detailed error analysis is especially important for this problem because the motion between pairs of frames is small and slight perturbations in its estimates can lead to large errors in 3D reconstruction. We focus on the following issues: physical sources of errors, their experimental and theoretical analysis, robust estimation techniques and measures for characterizing the quality of the final reconstruction. We derive a precise relationship between the error in the reconstruction and the error in the image correspondences. The error analysis is used to design a robust, recursive multiframe fusion algorithm using "stochastic approximation" as the framework since it is capable of dealing with incomplete information about errors in observations. Ratedistortion analysis is proposed for evaluating the quality of the final reconstruction as a function of the number of frames and the error in the image correspondences. Finally, to demonstrate the e#ectiveness of the algorithm, examples of depth reconstruction are shown for different video sequences.
New Statistical Models for RandomsPrecorrected PET Scans
 in Information Processing in Medical
, 2001
"... PET measurements are usually precorrected for accidental coincidence events by realtime subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for accidental coincidences but destroys the Poisson statistics. We propose and analyze two new approximations to the exa ..."
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Cited by 24 (19 self)
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PET measurements are usually precorrected for accidental coincidence events by realtime subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for accidental coincidences but destroys the Poisson statistics. We propose and analyze two new approximations to the exact loglikelihood of the precorrected measurements, one based on a "shifted Poisson" model, the other based on saddlepoint approximations to the measurement probability mass function (pmf). The methods apply to both emission and transmission tomography; however in this paper we focus on transmission tomography. We compare the new models to conventional dataweighted least squares (WLS) and conventional maximum likelihood (based on the ordinary Poisson (OP) model) using simulations and analytic approximations. The results demonstrate that the proposed methods avoid the systematic bias of the WLS method, and lead to significantly lower variance than the conventional OP method. The saddlepoint method provides a more accurate approximation to the exact loglikelihood than the WLS, OP and shifted Poisson alternatives.
PenalizedLikelihood Estimators and Noise Analysis for RandomsPrecorrected PET Transmission Scans
 IEEE Tr. Med. Im
, 1999
"... This paper analyzes and compares image reconstruction methods based on practical approximations to the exact loglikelihood of randomsprecorrected PET measurements. The methods apply to both emission and transmission tomography; however in this paper we focus on transmission tomography. The results ..."
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Cited by 20 (11 self)
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This paper analyzes and compares image reconstruction methods based on practical approximations to the exact loglikelihood of randomsprecorrected PET measurements. The methods apply to both emission and transmission tomography; however in this paper we focus on transmission tomography. The results of experimental PET transmission scans and variance approximations demonstrate that the "shifted Poisson" (SP) method avoids the systematic bias of the conventional dataweighted least squares (WLS) method, and leads to significantly lower variance than conventional statistical methods based on the loglikelihood of the ordinary Poisson (OP) model. We develop covariance approximations to analyze the propagation of noise from attenuation maps into emission images via the attenuation correction factors (ACFs). Empirical pixel and region variances from real transmission data agree closely with the analytical predictions. Both the approximations and the empirical results show that the performanc...
Resolution properties of regularized image reconstruction methods
 of EECS, Univ. of Michigan, Ann Arbor, MI
, 1995
"... This paper examines the spatial resolution properties of penalizedlikelihood image reconstruction methods by analyzing the local impulse response. The analysis shows that standard regularization penalties induce spacevariant local impulse response functions, even for spaceinvariant tomographic s ..."
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Cited by 20 (13 self)
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This paper examines the spatial resolution properties of penalizedlikelihood image reconstruction methods by analyzing the local impulse response. The analysis shows that standard regularization penalties induce spacevariant local impulse response functions, even for spaceinvariant tomographic systems. Paradoxically, for emission image reconstruction the local resolution is generally poorest in highcount regions. We show that the linearized local impulse response induced by quadratic roughness penalties depends on the object only through its projections. This analysis leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution. The modified penalty also provides a very practical method for choosing the regularization parameter to obtain a specified resolution in images reconstructed by penalizedlikelihood methods.
Ficaro, “Maximum Likelihood Transmission Image Reconstruction for Overlapping Transmission Beams
 IEEE Tr. Med. Im
, 2000
"... In many transmission imaging geometries, the transmitted “beams ” of photons overlap on the detector, such that a detector element may record photons that originated in different sources or source locations and thus traversed different paths through the object. Examples include systems based on sc ..."
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Cited by 19 (8 self)
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In many transmission imaging geometries, the transmitted “beams ” of photons overlap on the detector, such that a detector element may record photons that originated in different sources or source locations and thus traversed different paths through the object. Examples include systems based on scanning line sources or on multiple parallel rod sources. The overlap of these beams has been disregarded by both conventional analytical reconstruction methods as well as by previous statistical reconstruction methods. We propose a new algorithm for statistical image reconstruction of attenuation maps that explicitly accounts for overlapping beams in transmission scans. The algorithm is guaranteed to monotonically increase the objective function at each iteration. The availability of this algorithm enables the possibility of deliberately increasing the beam overlap so as to increase count rates. Simulated SPECT transmission scans based on a multiple line source array demonstrate that the proposed method yields improved resolution/noise tradeoffs relative to “conventional ” reconstruction algorithms, both statistical and nonstatistical. I.
ÒCovariance approximation for fast and accurate computation of channelized Hotelling observer statistics,Ó
 IEEE Tr. Nuc. Sci
, 2000
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