Low-Rank Tensor Decomposition With Smooth and Sparse Regularization for Hyperspectral and Multispectral Data Fusion

Abstract

The fusion of hyperspectral and multispectral images is an effective way to obtain hyperspectral super-resolution images with high spatial resolution. A hyperspectral image is a datacube containing two spatial dimensions and a spectral dimension. The fusion methods based on non-negative matrix factorization need to reshape the three-dimensional data in matrix form, which will result in the loss of data structure information. Owing to the non-uniqueness of tensor rank and noise inference, there is a lot of redundant information in the spatial and spectral subspaces of tensor decomposition. To address the above problems, this article incorporates smooth and sparse regularization into low-rank tensor decomposition to reformulate a fusion method, in which the logarithmic sum function is adopted to eliminate the effect of redundant information and shadows in both spatial and spectral domains. Moreover, the total-variationbased regularizer is employed to vertically smooth the spectral factor matrix to suppress the noise. Then, the alternating direction multiplier method, as well as the conjugate gradient approach, is utilized to design a set of efficient algorithms by complexity reduction. The experimental results demonstrate that the proposed method can yield better performance than the state-of-the-art benchmark algorithms in most cases, which also verifies the effectiveness of incorporated regularizers in low signal-to-noise ratio environments for hyperspectral super-resolution images.

NMF-DuNet: Nonnegative Matrix Factorization Inspired Deep Unrolling Networks for Hyperspectral and Multispectral Image Fusion

“…Matrix factorization-based for LrHSI-HrMSI methods assume the desired HrHSI can be reconstructed by a few spectral atoms multiplied by its corresponding coefficient [27], [28], [30]. Therefore the fusion problem can be solved by estimating the spectral endmember from the LrHSI and then using a sparse coding algorithm to estimate the abundance matrix from HrMSI with sparse prior regularization [31].…”

“…Relatively homogenous pixels were supposed to be comparable due to spatial coherence; nevertheless, these pixels disperse the spectral basis in the LrHSI endmembers, thereby ensuring spatial uniformity. Furthermore, Ma et al [28] devised a method by combining smooth and sparse priors on low-rank tensor factorization for reformulating fusion, wherein the logarithmic sum restriction was utilized for removing superfluous information in equally spectral and spatial dominions. Furthermore, a total variationsbased regularizer was adapted for smoothing the spectral factor matrix to suppress the noise.…”

Graph-Based Logarithmic Low-Rank Tensor Decomposition for the Fusion of Remotely Sensed Images

“…The stopping rule satisfies the relative difference threshold between the successive updates of the objective function 𝑓 (W, H, A, C) is less than 0.001. The experiments show that changing the number of iterations in the ADMMbased algorithms has little effect on the convergence of the whole algorithm [20] [21]. That is, the variables of W, H, A and C do not run exhaustively for convergence.…”

“…Another popular methods can achieve the HSI-MSI fusion via tensor decomposition without destroying the original data structure. The common forms of tensor decomposition include Canonical polyadic decomposition (CPD) [20] and Tucker decomposition [21]. For example, Kanatsoulis et al [22] proposed a CPD-based coupled tensor decomposition model and performed the fusion performance in the case where the degrading operator was unknown.…”

“…Zhang et al [25] designed a super-resolution method based on Tucker tensor decomposition and joint spatial-spectral-graph regularization. Ma et al [21] put forward a Tucker-based model by imposing low-rank and sparsity regularization on factor matrices and core tensor,respectively. Since Tucker decomposition can keep the three-dimensional data cube unchanged during processing, there is no loss of structural information.…”