Abstract
The problem of tomographic image reconstruction can be reduced to an optimization problem of finding unknown pixel values subject to minimizing the difference between the measured and forward projections. Iterative image reconstruction algorithms provide significant improvements over transform methods in computed tomography. In this paper, we present an extended class of power-divergence measures (PDMs), which includes a large set of distance and relative entropy measures, and propose an iterative reconstruction algorithm based on the extended PDM (EPDM) as an objective function for the optimization strategy. For this purpose, we introduce a system of nonlinear differential equations whose Lyapunov function is equivalent to the EPDM. Then, we derive an iterative formula by multiplicative discretization of the continuous-time system. Since the parameterized EPDM family includes the Kullback–Leibler divergence, the resulting iterative algorithm is a natural extension of the maximum-likelihood expectation-maximization (MLEM) method. We conducted image reconstruction experiments using noisy projection data and found that the proposed algorithm outperformed MLEM and could reconstruct high-quality images that were robust to measured noise by properly selecting parameters.
Highlights
Image reconstruction in computed tomography (CT) is the process of estimating unknown density images from measured projections
We present an extended class of power-divergence measures [21,22,23,24] (PDMs) and derive a novel iterative algorithm based on the minimization of the extended PDM (EPDM) as an objective function for the optimization strategy
We presented an extension the PDMbased familyonwith two parameters, γ and α, and proposed a novel iterativeofalgorithm minimization of the divergence measure proposed a novel iterative algorithm based on minimization of the divergence measure y 21, 2021 submitted to Entropy
Summary
Image reconstruction in computed tomography (CT) is the process of estimating unknown density images from measured projections. Is as follows: it enables us to prove the stability of the equilibrium corresponding to the desired solution of the system of differential equations by using the Lyapunov stability theorem [40] if a proper Lyapunov function can be found; since the step-size used to discretize the set of differential equations corresponds to the relaxation or scaling parameter of the system of difference equations, a family of iterative algorithms incorporating a parameter for acceleration is naturally derived It provides a methodology for systematically designing a new iterative reconstruction algorithm based on optimization of an objective function depending on the features of the image to be reconstructed. We conducted image reconstruction experiments using numerical and physical phantoms with noisy projections and found that the proposed algorithm outperformed the conventional MLEM method with respect to reconstructing high-quality images that are robust to measured noise when selecting a set of proper parameter values
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