Non-convex regularization in remote sensing

TL;DR

This paper investigates the effects of various regularizers, including nonconvex ones, on high-dimensional image classification and unmixing, providing insights and tools for optimal regularizer selection.

Contribution

It offers a comparative analysis of traditional and nonconvex regularizers in remote sensing tasks and supplies a practical toolbox for researchers.

Findings

Nonconvex regularizers can outperform traditional norms in certain tasks.

The choice of regularizer significantly impacts classification and unmixing performance.

Guidelines for selecting appropriate regularizers are provided.

Abstract

In this paper, we study the effect of different regularizers and their implications in high dimensional image classification and sparse linear unmixing. Although kernelization or sparse methods are globally accepted solutions for processing data in high dimensions, we present here a study on the impact of the form of regularization used and its parametrization. We consider regularization via traditional squared (2) and sparsity-promoting (1) norms, as well as more unconventional nonconvex regularizers (p and Log Sum Penalty). We compare their properties and advantages on several classification and linear unmixing tasks and provide advices on the choice of the best regularizer for the problem at hand. Finally, we also provide a fully functional toolbox for the community.