A computational framework for edge-preserving regularization in dynamic inverse problems

A Computational Framework for Inverse Queries in Statistical Learning Problems

This dissertation addresses the problem of inverting the nonlinear functions that arise in solutions to statistical learning problems. Such problems arise when inverse queries need to be answered. To provide background for the kinds of inverse queries that can arise in learning, we rst brie y present, as examples of the forward problem, the three most common learning problems arising in applica...

Regularization and Inverse Problems

An overview is given of Bayesian inversion and regularization procedures. In particular, the conceptual basis of the maximum entropy method (MEM) is discussed, and extensions to positive/negative and complex data are highlighted. Other deconvolution methods are also discussed within the Bayesian context, focusing mainly on the comparison of Wiener filtering, Massive Inference and the Pixon meth...

Deterministic edge-preserving regularization in computed imaging

Many image processing problems are ill-posed and must be regularized. Usually, a roughness penalty is imposed on the solution. The difficulty is to avoid the smoothing of edges, which are very important attributes of the image. In this paper, we first give conditions for the design of such an edge-preserving regularization. Under these conditions, we show that it is possible to introduce an aux...

Sparsity regularization in inverse problems

Edge-preserving Regularization in Image Restoration

The reconstruction of an image u(x, y) that describes a real scene from experimental data (observed image) I(x, y) can be identified as an inverse problem. This problem is generally ill-posed in the sense of Hadamard. The regularization of an inverse problem in image processing requires smoothing homogeneous areas of the object without degrading edges. The location of these edges are unknown an...