Multi-sensor data fusion of remotely-sensed images with sparse and logarithmic low-rank regularization for shadow removal and denoising

Abstract

ABSTRACT Hyperspectral images have high spectral resolution but low spatial resolution, which results in a large number of mixed pixels. As an economical and effective means to improve image quality, the fusion of hyperspectral and multispectral data from different sensors can achieve the reconstruction of super-resolution images. As a representative of fusion method, coupled non-negative matrix factorization is an ill-posed problem, in which the number of endmembers was set to be no less than the groundtruth without requiring an accurate value. However, this often results in spectral shadows and spatial information redundancy, especially when the observed images are contaminated by noise. To address these problems above, this article incorporates sparse and low-rank regularization to reformulate a bi-convex fusion problem for the removal of shadows and noise, in which the logarithmic sum function is employed to suppress the small singular components of endmember and abundance matrices. Then, an efficient solver is designed to obtain the closed-form solutions via matrix-vector operators, in which the alternating direction method of multipliers is utilized to split the variables using equality constraints. The experimental results of real datasets demonstrate that the proposed fusion method can effectively enhance the quality of reconstructed super-resolution images especially in high-noise environments, which also verifies the validation of incorporated regularization.