Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures

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.

Block-Iterative Reconstruction from Dynamically Selected Sparse Projection Views Using Extended Power-Divergence Measure

“…where γ and α, respectively, indicate positive and nonnegative parameters, which is a two-parameter extension [29] of the power-divergence measure and coincides with the KL-divergence if (γ, α) = (1, 1), the squared L 2 norm if (γ, α) = (1, 0), and so on. Lastly, we define…”

Noise Reduction Using Singular Value Decomposition with Jensen–Shannon Divergence for Coronary Computed Tomography Angiography

“…The thresholding of denoising by SVD requires the introduction of the effective evaluation function as a measure of the level of approximation between noise-free and noisy images. Methods using various evaluation functions have been proposed for CT image reconstruction, and their resulting high performances have been demonstrated [ 13 , 14 ]. Therefore, we used Jensen–Shannon (JS) divergence as an evaluation function for thresholding using low-rank approximation.…”

Entropy in Image Analysis III

“…In [ 1 ], the problem of tomographic image reconstruction is addressed. In the proposed method, an extended class of power-divergence measures, which are including a large set of distances and relative entropy measures, are involved in an iterative reconstruction algorithm.…”

“…The authors introduced in the method a system of nonlinear differential equations based on Lyapunov functions. Actually, the resulting iterative algorithm proposed in [ 1 ] represents a natural extension of the maximum-likelihood expectation-maximization method.…”