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

Hyperspectral images(HSIs)with the high-resolution spectral information have been widely employed in many fields,such as resource detection,target recognition,and envi-ronmental monitoring.However,the increasing volume of HSIs brings great challenges to storage and transmission.Recently,snapshot compressive imaging(SCI)has received increasing attention.The SCI system samples a set of contiguous channels(e.g.,coded aperture compressive spectral imaging)to obtain 2D compressed measurements,greatly reducing the computational workload.For the subsequent application of HSIs,an indis-pensable step is to reconstruct HSIs from 2D measurements.The key of the reconstruc-tion method is to reasonably extract useful priors,such as sparsity,low-rank property,local smoothness,and nonlocal self-similarity.However,existing methods can not fully capture the low-rank property and fail to maintain the whole structure of HSIs.The con-tributions of this thesis include three aspects.1.Since HSIs can be naturally represented as third-order tensors,we reformulate the degradation model in the SCI system as a tensor-based form,which can friendly allow us to characterize the underlying low-rank structure of HSIs.2.We propose a global low-rank tensor optimization model with nonlocal plug-and-play(Pn P)regularizers(GNLR),which simultaneously explores the global low-rankness,nonlocal transformed sparsity,and nonlocal low-rankness.More specifically,three-direc-tional tensor nuclear norm is used to characterize the global correlation of the underlying HSI.Two implicit regularizers under the Pn P framework depict the inter-patch and intra-patch redundancy of similar patches of the coefficient tensor.3.We design an efficient alternating direction method of multipliers-based algorithm to solve the proposed model.Experimental results on four HSI datasets illustrate the su-periority of the GNLR in terms of evaluation indices and visual effects.