Enhancing Hyperspectral Images Compressive Sensing Reconstruction With Smooth Low-Rankness Joint Gradient Sparsity

The application of compressive sensing (CS) theory in hyperspectral images (HSI) reconstruction has been validated. The key to model-based reconstruction methods lies in effectively integrating prior knowledge of HSI. However, capturing multiple prior knowledge means that multiple regularization terms need to be set, which not only increases the complexity of the model but also reduces its stability. In this article, a model based on smooth low-rank joint gradient sparsity (SLJGS) is proposed to enhance the capability of HSI compressed sensing reconstruction. First, we propose a new model called the Smooth Spatial-spectral Low-rank Model (SSLR). Unlike most current models that treat the low-rankness and local smoothness of HSI as two separate regularization terms, SSLR uses only one regularization term. Additionally, the use of 2D gradient images introduces spatial-spectral correlation, while the constraint of Tucker rank allows for a more comprehensive capture of low-rank information across spatial and spectral dimensions. At the same time, to address the shortcomings of SSLR in capturing spatial features and sparsity, we design the Multi-dimensional Coupled Gradient Sparsity (MCGS) model to extract these features. The combination of one-dimensional spatial gradient images with a two-dimensional spatial-spectral gradient image fully captures the gradient sparsity across multiple dimensions. Additionally, it obtains the rich spatial structure information of HSI. The superiority of the proposed model is demonstrated through comparative experiments conducted on three datasets.