$L_{1/2}$-Regularized Deconvolution Network for the Representation and Restoration of Optical Remote Sensing Images

Optical remote sensing images of land cover are composed of many natural and man-made objects and thus exhibit rich image features ranging from low to high levels. Extracting such a wide range of features to represent the optical remote sensing images, beyond edge primitives, is a long-standing goal in the remote sensing and vision research community. The recently proposed deconvolution network (DN) can effectively learn and capture features in a variety of forms: low-level edges, midlevel edge junctions, high-level object parts, and complete objects. The approach is based on the convolutional decomposition of images under an L1 sparsity constraint. Unfortunately, the L1 regularizer cannot enforce further sparsity, hence limiting the practical efficacy of the DN in optical remote sensing representation and processing. In this paper, we extend the DN by incorporating the L1/2 sparsity constraint, which we name the L1/2-DN. The L1/2 regularizer not only induces sparsity but is also a better choice among Lq, (0<;q<;1) regularizers. Furthermore, the L1/2-DN algorithm is more efficient, provides a sparser representation, and results in more accurate recovery than the DN. We illustrate the utility of our method on a wide range of optical remote sensing images and compare our results to those yielded by other state-of-the-art methods.