To be or not to be convex? A study on regularization in hyperspectral image classification

Hyperspectral image classification has long been dominated by convex models, which provide accurate decision functions exploiting all the features in the input space. However, the need for high geometrical details, which are often satisfied by using spatial filters, and the need for compact models (i.e. relying on models issued form reduced input spaces) has pushed research to study alternatives such as sparsity inducing regularization, which promotes models using only a subset of the input features. Although successful in reducing the number of active inputs, these models can be biased and sometimes offer sparsity at the cost of reduced accuracy. In this paper, we study the possibility of using non-convex regularization, which limits the bias induced by the regularization. We present and compare four regularizers, and then apply them to hyperspectral classification with different cost functions.