Joint Spatial-Spectral Smoothing in a Minimum-Volume Simplex for Hyperspectral Image Super-Resolution

Abstract

The limitations of hyperspectral sensors usually lead to coarse spatial resolution of acquired images. A well-known fusion method called coupled non-negative matrix factorization (CNMF) often amounts to an ill-posed inverse problem with poor anti-noise performance. Moreover, from the perspective of matrix decomposition, the matrixing of remotely-sensed cubic data results in the loss of data’s structural information, which causes the performance degradation of reconstructed images. In addition to three-dimensional tensor-based fusion methods, Craig’s minimum-volume belief in hyperspectral unmixing can also be utilized to restore the data structure information for hyperspectral image super-resolution. To address the above difficulties simultaneously, this article incorporates the regularization of joint spatial-spectral smoothing in a minimum-volume simplex, and spatial sparsity—into the original CNMF, to redefine a bi-convex problem. After the convexification of the regularizers, the alternating optimization is utilized to decouple the regularized problem into two convex subproblems, which are then reformulated by separately vectorizing the variables via vector-matrix operators. The alternating direction method of multipliers is employed to split the variables and yield the closed-form solutions. In addition, in order to solve the bottleneck of high computational burden, especially when the size of the problem is large, complexity reduction is conducted to simplify the solutions with constructed matrices and tensor operators. Experimental results illustrate that the proposed algorithm outperforms state-of-the-art fusion methods, which verifies the validity of the new fusion approach in this article.