Global hard thresholding algorithms for joint sparse image representation and denoising

TL;DR

This paper introduces a new framework and two algorithms for joint sparse image representation and denoising that effectively allocate a global sparsity budget across image patches, improving scalability and performance.

Contribution

The paper proposes a novel joint sparse coding framework and two global hard thresholding algorithms based on variable splitting, addressing the distribution of sparsity across patches.

Findings

Effective sparse image representation and denoising demonstrated on synthetic and real data.

Algorithms show high scalability suitable for large megapixel images.

Proposed methods outperform traditional patch-wise approaches in efficiency and quality.

Abstract

Sparse coding of images is traditionally done by cutting them into small patches and representing each patch individually over some dictionary given a pre-determined number of nonzero coefficients to use for each patch. In lack of a way to effectively distribute a total number (or global budget) of nonzero coefficients across all patches, current sparse recovery algorithms distribute the global budget equally across all patches despite the wide range of differences in structural complexity among them. In this work we propose a new framework for joint sparse representation and recovery of all image patches simultaneously. We also present two novel global hard thresholding algorithms, based on the notion of variable splitting, for solving the joint sparse model. Experimentation using both synthetic and real data shows effectiveness of the proposed framework for sparse image representation and denoising tasks. Additionally, time complexity analysis of the proposed algorithms indicate high scalability of both algorithms, making them favorable to use on large megapixel images.