Adaptive hard-thresholding for linear inverse problems

Distributed Iterative Thresholding for ℓ0/ℓ1-Regularized Linear Inverse Problems

The `0/`1-regularized least squares approach is used to deal with linear inverse problems under sparsity constraints, which arise in mathematical and engineering fields, e.g., statistics, signal processing, machine learning, and coding theory. In particular, multi-agent models have been recently emerged in this context to describe diverse kinds of networked systems, ranging from medical databas...

A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems

We consider the class of iterative shrinkage-thresholding algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods, which can be viewed as an extension of the classical gradient algorithm, is attractive due to its simplicity and thus is adequate for solving large-scale problems even with dense matrix data. However, such methods are also kno...

Ill-Posed and Linear Inverse Problems

In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

Adaptive Wavelet Galerkin Methods for Linear Inverse Problems

We introduce and analyze numerical methods for the treatment of inverse problems, based on an adaptive wavelet Galerkin discretization. These methods combine the theoretical advantages of the wavelet-vaguelette decomposition (WVD) in terms of optimally adapting to the unknown smoothness of the solution, together with the numerical simplicity of Galerkin methods. In a first step, we simply combi...

Adaptive Wavelet Galerkin Methods for Linear Inverse Problems