Performance of First-Order Algorithms for TV Penalized Weighted Least-Squares Denoising Problem

Abstract

Denoising of images perturbed by non-standard noise models (e.g., Poisson or Gamma noise) can be often realized by a sequence of penalized weighted least-squares minimization problems. In the recent past, a variety of first-order algorithms have been proposed for convex problems but their efficiency is usually tested with the classical leastsquares data fidelity term. Thus, in this manuscript, first-order state-ofthe-art computational schemes are applied on a total variation penalized weighted least-squares denoising problem and their performance is evaluated on numerical examples simulating a Poisson noise perturbation.

First Order Algorithms in Variational Image Processing

“…The EM algorithm is a classically applied (iterative) reconstruction method in emission tomography [117,167]. The TV proximal problem was solved by an adopted variant of the modified Arrow-Hurwicz method proposed in [42] since it was shown to be the most efficient method for TV penalized weighted least-squares denoising problems in [145]. Furthermore, a warm starting strategy was used to initialize the dual variables within the TV proximal problem and the inner iteration sequence was stopped if the relative error of primal and dual optimality conditions was below an error tolerance δ, i.e., using the notations from [42], if…”

Accelerated fast iterative shrinkage thresholding algorithms for sparsity‐regularized cone‐beam CT image reconstruction

“…13,15 There are numerous algorithms 3,4,6-10,17-25 that have been developed to solve TV regularized image reconstruction problems. Modern optimization methods 11,12,[26][27][28][29][30][31][32][33] can be applied to a variety of reconstruction problems that employ nonsmooth regularizers. In this study, we seek to accelerate advanced FIS-TAs (Refs.…”

“…To consider the effect of the weighted matrix D −1 v , Eq. (A3) in Algorithm III needs to be modified 32 as…”

Color Bregman TV

“…Note that since we use the same convolution operator on each channel, the formulations (32) and (48) are equivalent. Hence we solve the first by applying a standard forward backward splitting method together with an ADMM solver for the backward problem as described in [41,40]. The results are illustrated again for Kodak image 23 in figure 6, where we used σ = 0.025 for u taking values between 0 and 1.…”

“…Hence we solve the first by applying a standard forward backward splitting method together with an ADMM solver for the backward problem as described in [41,40].…”