A theoretical study of the contrast recovery and variance of MAP reconstructions from PET data

Published on Apr 1, 1999in IEEE Transactions on Medical Imaging10.048
路 DOI :10.1109/42.768839
Jinyi Qi53
Estimated H-index: 53
(SC: University of Southern California),
Richard M. Leahy75
Estimated H-index: 75
(SC: University of Southern California)
Sources
Abstract
The authors examine the spatial resolution and variance properties of PET images reconstructed using maximum a posteriori (MAP) or penalized-likelihood methods. Resolution is characterized by the contrast recovery coefficient (CRC) of the local impulse response. Simplified approximate expressions are derived for the local impulse response CRCs and variances for each voxel. Using these results the authors propose a practical scheme for selecting spatially variant smoothing parameters to optimize lesion detectability through maximization of the local CRC-to-noise ratio in the reconstructed image.
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A Bayesian method is described for reconstruction of high-resolution 3D images from the microPET small-animal scanner. Resolution recovery is achieved by explicitly modelling the depth dependent geometric sensitivity for each voxel in combination with an accurate detector response model that includes factors due to photon pair non-collinearity and inter-crystal scatter and penetration. To reduce storage and computational costs we use a factored matrix in which the detector response is modelled u...
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#1Jeffrey A. Fessler (UM: University of Michigan)H-Index: 79
The authors present a fairly simple procedure for computing new approximations for the pixel variances in images reconstructed by penalized-likelihood methods. The method enables the display of variance images, which can provide an indication of uncertainty that may be helpful in medical diagnosis and in evaluation of image reconstruction algorithms. Simulations of positron emission tomography (PET) scans illustrate the accuracy of the proposed variance approximations in nonzero image pixels.
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#1Wenli Wang (SBU: Stony Brook University)H-Index: 2
#2Gene Gindi (SBU: Stony Brook University)H-Index: 26
The ability to theoretically model the propagation of photon noise through PET and SPECT tomographic reconstruction algorithms is crucial in evaluating the reconstructed image quality as a function of parameters of the algorithm. In a previous approach for the important case of the iterative ML - EM (maximum-likelihood - expectation-maximization) algorithm, judicious linearizations were used to model theoretically the propagation of a mean image and a covariance matrix from one iteration to the ...
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#1Dave Higdon (Duke University)H-Index: 19
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In recent years, many investigators have proposed Gibbs prior models to regularize images reconstructed from emission computed tomography data. Unfortunately, hyperparameters used to specify Gibbs priors can greatly influence the degree of regularity imposed by such priors and, as a result, numerous procedures have been proposed to estimate hyperparameter values, from observed image data. Many of these, procedures attempt to maximize the joint posterior distribution on the image scene. To implem...
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The parameters of the prior, the hyperparameters, play an important role in Bayesian image estimation. Of particular importance for the case of Gibbs priors is the global hyperparameter, /spl beta/, which multiplies the Hamiltonian. Here we consider maximum likelihood (ML) estimation of /spl beta/ from incomplete data, i.e., problems in which the image, which is drawn from a Gibbs prior, is observed indirectly through some degradation or blurring process. Important applications include image res...
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Accurate modeling of the data formation and detection process in PET is essential for optimizing resolution. Here, the authors develop a model in which the following factors are explicitly included: depth dependent geometric sensitivity, photon pair non-colinearity, attenuation, intrinsic detector sensitivity, non-uniform sinogram sampling, crystal penetration and inter-crystal scatter. Statistical reconstruction methods can include these modeling factors in the system matrix that represents the...
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This paper examines the spatial resolution properties of penalized-likelihood image reconstruction methods by analyzing the local impulse response. The analysis shows that standard regularization penalties induce space-variant local impulse response functions, even for space-invariant tomographic systems. Paradoxically, for emission image reconstruction, the local resolution is generally poorest in high-count regions. We show that the linearized local impulse response induced by quadratic roughn...
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We introduce a plane, which we call the delta-sigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a uniform Cramer-Rao (CR) bound on estimator variance, a delta-sigma tradeoff curve is specified that defines an "unachievable region" of the delta-sigma plane for a specified statistical model. In order ...
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Over the past years there has been considerable interest in statistically optimal reconstruction of cross-sectional images from tomographic data. In particular, a variety of such algorithms have been proposed for maximum a posteriori (MAP) reconstruction from emission tomographic data. While MAP estimation requires the solution of an optimization problem, most existing reconstruction algorithms take an indirect approach based on the expectation maximization (EM) algorithm. We propose a new appro...
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