2013/07/17 by Jérôme Fehrenbach, Fehrenbach, Jérôme, Pierre Weiss +1
Computer Science · Mathematics · #Applications (stat.AP) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Medical Image Segmentation Techniques #Optimization and Control (math.OC) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1307.4592
openalex publication_date 2013/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Additive or multiplicative stationary noise recently became an important\nissue in applied fields such as microscopy or satellite imaging. Relatively few\nworks address the design of dedicated denoising methods compared to the usual\nwhite noise setting. We recently proposed a variational algorithm to tackle\nthis issue. In this paper, we analyze this problem from a statistical point of\nview and provide deterministic properties of the solutions of the associated\nvariational problems. In the first part of this work, we demonstrate that in\nmany practical problems, the noise can be assimilated to a colored Gaussian\nnoise. We provide a quantitative measure of the distance between a stationary\nprocess and the corresponding Gaussian process. In the second part, we focus on\nthe Gaussian setting and analyze denoising methods which consist of minimizing\nthe sum of a total variation term and an l2 data fidelity term. While the\nconstrained formulation of this problem allows to easily tune the parameters,\nthe Lagrangian formulation can be solved more efficiently since the problem is\nstrongly convex. Our second contribution consists in providing analytical\nvalues of the regularization parameter in order to approximately satisfy\nMorozov's discrepancy principle.\n