Sparse Representation of Astronomical Images

TL;DR

This paper explores sparse representation techniques for astronomical images, demonstrating that mixed dictionaries and greedy algorithms like Orthogonal Matching Pursuit significantly improve sparsity and processing efficiency.

Contribution

It introduces a novel approach combining mixed dictionaries with greedy algorithms, including a refined Self Projected Matching Pursuit, for efficient sparse approximation of large astronomical images.

Findings

Achieves significant sparsity gains with mixed dictionaries.

Demonstrates efficiency of greedy algorithms for large images.

Introduces Self Projected Matching Pursuit for improved approximation.

Abstract

Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies. Experiments are conducted to confirm: i)Effectiveness at producing sparse representations. ii)Competitiveness, with respect to the time required to process large images.The latter is a consequence of the suitability of the proposed dictionaries for approximating images in partitions of small blocks.This feature makes it possible to apply the effective greedy selection technique Orthogonal Matching Pursuit, up to some block size. For blocks exceeding that size a refinement of the original Matching Pursuit approach is considered. The resulting method is termed Self Projected Matching Pursuit, because is shown to be effective for implementing, via Matching Pursuit itself, the optional back-projection intermediate steps in that approach.