Regularizing parameter estimation for Poisson noisy image restoration

Abstract

Deblurring images corrupted by Poisson noise is a challenging process which has devoted much research in many applications such as astronomical or biological imaging. This problem, among others, is an ill-posed problem which can be regularized by adding knowledge on the solution. Several methods have therefore promoted explicit prior on the image, coming along with a regularizing parameter to moderate the weight of this prior. Unfortunately, in the domain of Poisson deconvolution, only a few number of methods have been proposed to select this regularizing parameter which is most of the time set manually such that it gives the best visual results. In this paper, we focus on the use of l 1-norm prior and present two methods to select the regularizing parameter. We show some comparisons on synthetic data using classical image fidelity measures.

New convergence results for the scaled gradient projection method

“…The choice of the regularization parameter in Poisson data inversion is an active field and several different strategies have been proposed in the last years [46,38,47,48,49]. Here we consider that proposed by Bertero et al [38], which consists of selecting the value of ν in (32) such that…”

Post-reconstruction deconvolution of PET images by total generalized variation regularization

“…To ensure the convergence, condition στ L 2 2 < 1 has to be verified [12]. The choice of the regularization parameter is based on the discrepancy principle for Poisson noise adapted in [16] to images with null background. Parameter λ is selected such that…”

Relaxed ordered subset preconditioned alternating projection algorithm for PET reconstruction with automated penalty weight selection

“…At present, several researchers have developed theoretical frameworks based on the discrepancy principle (DP) given Gaussian and Poisson noise for estimating the penalty weights of single parameters. [28][29][30][31] The DP is the idea that the uncertainty of the data should match the variability of the object or penalty function. However, it has been pointed out by several researchers that this match does not necessarily result in a minimum mean squared error (MMSE) image, 32,33 nor if MMSE is necessarily the right goal.…”

“…), data from that class member, and a particular image quality metric, there were no simple theoretical means with which to choose the optimal penalty weights. At present, several researchers have developed theoretical frameworks based on the discrepancy principle (DP) given Gaussian and Poisson noise for estimating the penalty weights of single parameters …”