Convolutional group-sparse coding and source localization

TL;DR

This paper introduces a novel interpretation of convolutional coding as blind deconvolution with spatially varying point spread functions, offering a new optimization framework for source localization in scientific imaging.

Contribution

It generalizes previous non-negative group sparsity models for convolutional problems and connects them to source localization in scientific imaging applications.

Findings

Provides a new interpretation of convolutional coding as blind deconvolution.

Proposes a generalized optimization framework for these problems.

Demonstrates application on Hubble telescope data.

Abstract

In this paper, we present a new interpretation of non-negatively constrained convolutional coding problems as blind deconvolution problems with spatially variant point spread function. In this light, we propose an optimization framework that generalizes our previous work on non-negative group sparsity for convolutional models. We then link these concepts to source localization problems that arise in scientific imaging and provide a visual example on an image derived from data captured by the Hubble telescope.