Hyperspectral Image Super-Resolution via Nonlocal Low-Rank Tensor Approximation and Total Variation Regularization

Abstract

Hyperspectral image (HSI) possesses three intrinsic characteristics: the global correlation across spectral domain, the nonlocal self-similarity across spatial domain, and the local smooth structure across both spatial and spectral domains. This paper proposes a novel tensor based approach to handle the problem of HSI spatial super-resolution by modeling such three underlying characteristics. Specifically, a noncovex tensor penalty is used to exploit the former two intrinsic characteristics hidden in several 4D tensors formed by nonlocal similar patches within the 3D HSI. In addition, the local smoothness in both spatial and spectral modes of the HSI cube is characterized by a 3D total variation (TV) term. Then, we develop an effective algorithm for solving the resulting optimization by using the local linear approximation (LLA) strategy and the alternative direction method of multipliers (ADMM). A series of experiments are carried out to illustrate the superiority of the proposed approach over some state-of-the-art approaches.

Hyperspectral Image Super-Resolution with 1D–2D Attentional Convolutional Neural Network

“…Then, the regularization based methods is proposed to employ the image statistical distribution as prior, and regularize the solution space using prior assumptions. For instance, Paterl proposed an algorithm employing the discrete wavelet transform through using a sparsity-based regularization framework [4] and Wang et al proposed an algorithm based on TV-regularization and low-rank tensor [5]. Sub-pixel mapping [23,24] and self-similarity based [25] algorithms are also utilized for dealing with this problem.…”

“…However, due to complex details in HSIs, these algorithms with shallow heuristic models may cause spectral distortion. These algorithms can be used to enhance the spatial resolution of the spatial resolution of HSI in a band-by-band manner [5], which ignores the correlation of the band.…”

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

“…We can see that some variables, i.e., (18) and (19), have the same theoretical complexity, but their PRTs vary greatly owing to the sparsity and structure of the matrices. The theoretical complexity of a j+1 is reduced by only one OM between equations (21a) and (22), but the running time of a j+1 is greatly improved owing to structured matrices. However, in spite of the complexity decrease of three OMs, the improvement of b j+1 in running time is almost negligible, given that M and N are far less than L. Without the reduction in complexity described above, the proposed JSMV-CNMF algorithm would take at least 3000 s. Furthermore, comparing the time complexity of all methods, the running time is listed in Table 5 for two datasets.…”

“…As is well known, HSIs and MSIs are both cubic data, which can be considered three-dimensional tensors. Recently, another category of state-of-the-art method has been developed on basis of tensor decomposition, and includes canonical polyadic decomposition (CPD) [18,19] and Tucker decomposition [20][21][22], which can retain the cubic structure information of remote sensing images. For example, Li et al [20] proposed a fusion algorithm based on coupled sparse tensor factorization (CSTF), which was reformulated as the iterations of a core tensor and dictionaries of the three modes.…”

“…Charilaos et al [19] brought forward a CPD-based fusion framework, in which the identifiability of the reconstructed image was discussed under mild conditions. Wang et al [22] proposed a tensor-based approach to handle the problem of HSI spatial super-resolution by incorporating the regularizers of nonlocal low-rank tensor approximation and total variation. However, as the rank-1 version of Tucker decomposition [23], CPD is usually used to describe linear local features in the image, rather than complex features.…”