Reconstruction Algorithm For Emission Tomography Research Articles

Comparative Studies on Various Iterative Image Reconstruction Algorithms for Emission Tomography

Comparative Studies on Various Iterative Image Reconstruction Algorithms for Emission Tomography

Noise propagation for iterative penalized-likelihood image reconstruction based on Fisher information

Iterative reconstruction algorithms have been widely used in PET and SPECT emission tomography. Accurate modeling of photon noise propagation is crucial for quantitative tomography applications. Iteration-based noise propagation methods have been developed for only a few algorithms that have explicit multiplicative update equations. And there are discrepancies between the iteration-based methods and Fessler's fixed-point method because of improper approximations. In this paper, we present a unified theoretical prediction of noise propagation for any penalized expectation maximization (EM) algorithm where the EM approach incorporates a penalty term. The proposed method does not require an explicit update equation. The update equation is assumed to be implicitly defined by a differential equation of a surrogate function. We derive the expressions using the implicit function theorem, Taylor series and the chain rule from vector calculus. We also derive the fixed-point expressions when iterative algorithms converge and show the consistency between the proposed method and the fixed-point method. These expressions are solely defined in terms of the partial derivatives of the surrogate function and the Fisher information matrices. We also apply the theoretical noise predictions for iterative reconstruction algorithms in emission tomography. Finally, we validate the theoretical predictions for MAP-EM and OSEM algorithms using Monte Carlo simulations with Jaszczak-like and XCAT phantoms, respectively.

Optimization of 2D image reconstruction for positron emission mammography using IDL

The Clear-PEM system is a prototype machine for Positron Emission Mammography (PEM) under development within the Portuguese PET-Mammography consortium. We have embedded 2D image reconstruction algorithms implemented in IDL within the prototype's image analysis package. The IDL implementation of these algorithms proved to be accurate and computationally efficient. In this paper, we present the implementation of the MLEM, OSEM and ART 2D iterative image reconstruction algorithms for PEM using IDL. C and IDL implementations are compared using realistic Monte Carlo simulated data. We show that IDL can be used for the easy implementation of image reconstruction algorithms for emission tomography.

Simultaneous reconstruction and edge detection of tomographic images using accelerated deterministic annealing

We introduce fast image reconstruction algorithms for emission tomography, which provide not only edge-preserved reconstructions, but also their edge maps simultaneously. To explicitly model the existence of edges, we use the binary line-process model, which is incorporated as a Gibbs prior in the context of a Bayesian maximum a posteriori framework. To efficiently handle the problem of mixed continuous and binary variable objectives, we use a deterministic annealing (DA) algorithm. Since the DA algorithm is computer-intensive and requires many iterations to converge, we apply a block-iterative method derived from the well-known ordered-subset principle. The block-iterative DA algorithm processes the data in blocks within each iteration, thereby accelerating the convergence speed of the standard DA algorithm by a factor proportional to the number of blocks. Our experimental results indicate that, with moderate numbers of blocks and properly chosen hyperparameters, the accelerated DA algorithm provides good reconstructions as well as edge maps with only a few iterations.

Analytic reconstruction algorithms in emission tomography with variable attenuation

Analytic reconstruction algorithms in emission tomography with variable attenuation

Performance comparison of convex-nonquadratic priors for Bayesian tomographic reconstruction

Bayesian methods have formed the core of the development of reconstruction algorithms for emission tomography. In particular, there has been considerable interest in edge-preserving prior models, which are associated with smoothing penalty functions that are nonquadratic functions of nearby pixel differences. In spite of several advantages of nonconvex prior models, their use in routine applications has been hindered by several factors, such as the computational expense due to the nonconvexity of penalty functions and the difficulty in the selection of hyperparameters. We note here that, by choosing a penalty function which is nonquadratic but is still convex, both the problem of nonconvexity involved in some nonquadratic priors and the edge-oversmoothing problem of conventional quadratic priors may be avoided. In this paper, we use a class of two-dimensional smoothing splines with low (first) and high (second) spatial derivatives applied to convex-nonquadratic (CNQ) penalty functions. To compare quantitative performance of our new priors, we use the quantitation of bias/variance and total squared error over noise trials. Our numerical results show that a linear combination of first- and second-order spatial derivatives applied to CNQ penalty functions improves reconstructions in terms of total squared error.

Maximum likelihood image reconstruction in positron emission tomography (PET):\sConvergence characteristics and stopping rules

Maximum likelihood estimation image reconstruction algorithms for emission tomography received much attention during the last decade because of their potential to produce high quality images.\sA detailed study of the convergence properties of the expectation–maximization (EM) algorithm for PET image reconstruction is presented.\sThe main problems associated with this technique are addressed, namely, its high computational cost and the lack of a robust stopping criterion for this iterative algorithm.\sA practical implementation of the EM algorithm on a modern workstation is presented.\sA PET scanner is simulated using Monte Carlo techniques.\sDifferent kinds of data sets are produced and used in order to study the properties of the algorithm and develop a stopping rule, which are then validated with the use of real sinogram data from a commercial PET scanner.\sOther algorithms of the same iterative class are studied and modified versions of the EM algorithm are proposed with stopping rules, all based on the properties of the image vector updating coefficients in each iteration.\sA practical implementation of the EM algorithm is the final result, with optimal performance on the conventional computing systems available today, producing tomographic reconstructions in clinically meaningful times.

Solving emission tomography problems on vector machines

Shepp and Vardi's maximum likelihood reconstruction algorithm for emission tomography has mostly been ignored by the medical community because of its perceived high computational costs. However, the algorithm is very suited to parallel and vector machines, and on these machine can be made economically feasible even on medically reasonable problems of 16000 variables. It is also a good test problem for parallel optimization algorithms for large simply bounded nonlinear problems.

A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.

Statistically based image reconstruction for emission tomography

AbstractThis paper presents the motivation, development, algorithms, and performance tests of some fundamental statistically based reconstruction algorithms in emission tomography (ET). The motivation is based on an analysis of the filtered backprojection method (FBP) of reconstruction as a statistical process in which it is shown that it corresponds to the wrong statistical distribution for the ET problem. The development of the target functions and algorithms for the maximum likelihood estimator method (MLE) and for a Bayesian method with entropy prior is shown in a manner consistent with the FBP analysis. The concept of a “feasible” image is discussed as a necessary condition for a reconstruction to be acceptable and the choice of a uniform image field as the initial guess for the iterative methods is justified in terms of the lack of prior information on the image to be reconstructed. Finally, a number of image and profile comparisons are presented in which the feasible images obtained by the above methods, and by the method of sieves, appear superior to FBP images. Real data from the ECAT‐III tomography are used for all the reconstruction.

Implementing and Accelerating the EM Algorithm for Positron Emission Tomography

Since the publication of Shepp and Vadi's [ 14] maximum likelihood reconstruction algorithm for emission tomography (ET), many medical research centers engaged in ET have made an effort to change their reconstruction algorithms to this new approach. Some have succeeded, while others claim they could not adopt this new approach primarily because of limited computing power. In this paper, we discuss techniques for reducing the computational requirements of the reconstruction algorithm. Specifically, the paper discusses the data structures one might use and ways of taking advantage of the geometry of the physical system. The paper also treats some of the numerical aspects of the EM (expectation maximization) algorithm, and ways of speeding up the numerical algorithm using some of the traditional techniques of numerical analysis.