Quality Versus Sparsity in Image Recovery by Dictionary Learning Using Iterative Shrinkage

TL;DR

This paper investigates the balance between sparsity and quality in image recovery using dictionary learning, showing that high sparsity does not necessarily reduce recovery quality across different optimization methods.

Contribution

It analyzes how various optimization methods influence sparsity regimes and demonstrates that high sparsity can be achieved without compromising image recovery quality.

Findings

Different sparsity regimes depend on the optimization method used.

High sparsity solutions can still yield high-quality image recovery.

Sparsity does not always correlate with similarity to the learning database.

Abstract

Sparse dictionary learning (SDL) is a fundamental technique that is useful for many image processing tasks. As an example we consider here image recovery, where SDL can be cast as a nonsmooth optimization problem. For this kind of problems, iterative shrinkage methods represent a powerful class of algorithms that are subject of ongoing research. Sparsity is an important property of the learned solutions, as exactly the sparsity enables efficient further processing or storage. The sparsity implies that a recovered image is determined as a combination of a number of dictionary elements that is as low as possible. Therefore, the question arises, to which degree sparsity should be enforced in SDL in order to not compromise recovery quality. In this paper we focus on the sparsity of solutions that can be obtained using a variety of optimization methods. It turns out that there are different sparsity regimes depending on the method in use. Furthermore, we illustrate that high sparsity does in general not compromise recovery quality, even if the recovered image is quite different from the learning database.