Low-Rank Tensor Optimization With Nonlocal Plug-and-Play Regularizers for Snapshot Compressive Imaging

Abstract

The increasing volume of hyperspectral images (HSIs) brings great challenges to storage and transmission. Recently, snapshot compressive imaging (SCI), which compresses 3D HSIs into 2D measurements, has received increasing attention. Since the original HSIs can be naturally represented as thirdorder tensors, in this work, we reformulate the degradation model in the SCI systems as a tensor-based form, which friendly allows us to explore the underlying low-rank tensor structure of HSIs. To address the ill-posed SCI reconstruction problem, we suggest a global low-rank tensor optimization model with nonlocal plugand-play (PnP) regularizers (GNLR) to reconstruct the HSI from the 2D measurement, which flexibly and collaboratively integrates three-directional tensor nuclear norm (3DTNN) and two implicit nonlocal regularizers. More concretely, 3DTNN characterizes the global correlation of the underlying HSIs. Two implicit regularizers under the PnP framework exploit the benefits of the transformed sparse and low-rank priors on similar patches of the coefficient tensor, respectively. Based on the alternating direction method of multipliers (ADMM) algorithm, we develop an efficient algorithm to tackle the proposed model. Extensive experiments on remotely sensed HSIs and real-world HSIs demonstrate the superiority of the proposed GNLR method.

Spectral Quadratic Variation Regularized Autoweighted Tensor Ring Decomposition for Hyperspectral Image Reconstruction

“…The RGB images of the PaviaU dataset, the Reno dataset, and the CAVET dataset. [14], GNLR [29], and NGMeet [34]. All the comparison algorithms apply the same compression operator as the proposed SQV-AwTR model.…”

“…Fan et al [28] formulated a low-rank tensor recovery (LRTR) model based on the tubal rank-related TNN to characterize the 3D structural complexity of multilinear data. GNLR [29] employed 3DTNN [30] to preserve the structural information of the original data in spatial and spectral domains, as the matrix factorization destroys the inherent structure of a third-order tensor. These two kinds of low-rank tensor decomposition have been combined in HSI missing data recovery.…”

Multishot Compressive Hyperspectral Imaging Based on Tensor Fibered Rank Minimization and Its Primal-Dual Algorithm

“…However, the reconstruction results of these methods remain unsatisfactory, such as excessive smoothing phenomenon. To improve the reconstruction performance, more effective priors have been developed, including nonlocal self-similarity [16] based on weighted nuclear norm minimization, and spatial nonlocal self-similarity integrated with global spectral correlation of HSI [35]. To solve these objective optimization problems, the alternating direction method of multiplier (ADMM) [35] has become the most popular method.…”

“…To improve the reconstruction performance, more effective priors have been developed, including nonlocal self-similarity [16] based on weighted nuclear norm minimization, and spatial nonlocal self-similarity integrated with global spectral correlation of HSI [35]. To solve these objective optimization problems, the alternating direction method of multiplier (ADMM) [35] has become the most popular method. Nevertheless, those ADMM based methods [16], [35] have special requirements on the sensing matrix and are mainly designed for the single snapshot CASSI mechanism, which makes them inflexible.…”

“…To solve these objective optimization problems, the alternating direction method of multiplier (ADMM) [35] has become the most popular method. Nevertheless, those ADMM based methods [16], [35] have special requirements on the sensing matrix and are mainly designed for the single snapshot CASSI mechanism, which makes them inflexible.…”