Accurate Multiobjective Low-Rank and Sparse Model for Hyperspectral Image Denoising Method

Due to the unavoidable influence of sparse and Gaussian noise during the process of data acquisition, the quality of hyperspectral images (HSIs) is degraded and their applications are greatly limited. It is therefore necessary to restore clean HSIs. In the traditional methods, low-rank and sparse matrix decomposition methods are usually applied to restore the pure data matrix from the observed data matrix. However, due to the fact that the optimization of the
${l}_{0}$
-norm for the sparse modeling is a nonconvex and NP-hard problem, convex relaxation and regularization parameters are usually introduced. However, convex relaxation often leads to inaccurate sparse modeling results, and the sensitive regularization parameters can lead to unstable results. Thus, in this article, to address these issues, an accurate multiobjective low-rank and sparse denoising framework is proposed for HSIs to achieve accurate modeling. The
${l}_{0}$
-norm is directly modeled as the sparse noise and is optimized by an evolutionary algorithm, and the denoising problem is converted into a multiobjective optimization problem through simultaneously optimizing the low-rank term, the sparse term, and the data fidelity term, without sensitive regularization parameters. However, since the low-rank clean image and sparse noise of the HSI are encoded into a solution, the length of the solution is too long to be optimized. In this article, a subfitness strategy is constructed to achieve effective optimization by comparing the objective function values corresponding to each band for each solution. The experiments undertaken with simulated images in 11 noise cases and four real noisy images confirm the effectiveness of the proposed method.