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

The increasing volume of hyperspectral images (HSIs) brings great challenges to storage and transmission. Recently, snapshot compressive imaging (SCI), which compresses 3-D HSIs into 2-D measurements, has received increasing attention. Since the original HSIs can be naturally represented as third-order 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 plug-and-play (PnP) regularizers (GNLR) to reconstruct the HSI from the 2-D 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 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.