Multiobjective Sparse Subpixel Mapping for Remote Sensing Imagery

Abstract

Subpixel mapping (SPM) of remote sensing imagery is aimed at generating a classification map with a finer spatial resolution based on the abundance maps. The sparse subpixel mapping (SSM) method reformulates the SPM problem into a spatial pattern linear regression problem based on the preconstructed subpixel patch dictionary. However, in the SSM model, the optimization of the ${L}0$ -norm is a nonconvex NP-hard problem, so the ${L}1$ -norm is used to replace the ${L}0$ -norm to obtain an approximate solution, and the selection of the optimal weight parameter between multiple terms is difficult. Thus, in this paper, a novel multiobjective SSM (MOSSM) framework for remote sensing imagery is proposed, which transforms the SSM problem into a multiobjective optimization problem. In MOSSM, first, the sparsity term is accurately modeled using the ${L}0$ -norm instead of the ${L}1$ -norm to avoid the potential errors caused by the ${L}1$ -norm, and an evolutionary algorithm is used to directly optimize the ${L}0$ -norm. Second, a subfitness-based multiobjective evolutionary algorithm is employed to simultaneously optimize the fidelity term, the sparsity term, and the spatial prior term, and to generate a set of optimal sparse coefficients to balance these three terms. Thus, there is no need to determine sensitive weight parameters. Finally, two spatial prior terms, which can be applied to the overcomplete dictionary, are presented in the proposed MOSSM-TV and MOSSM-L algorithms to incorporate the spatial correlation of subpixels. Experiments were conducted with two synthetic images and two real data sets, and the results were compared with those of ten other SPM algorithms to demonstrate the effectiveness of the proposed method.