Hyperspectral images reconstruction based on multi-angle hybrid tensor rank and gradient sparsity

Compressive sensing (CS) theory is widely applied in the compression and storage of hyperspectral images (HSI). A key issue in the application of HSI is how to accurately reconstruct images. Tensor-based methods typically utilize a single tensor decomposition combined with other regularization terms to capture the priors of HSI. However, capturing more comprehensive prior knowledge and reasonably combining them in a unified framework to achieve high-quality image reconstruction is a challenging problem. In this article, we propose a novel model based on multi-angle hybrid tensor rank and gradient sparsity (MAHTRGS) for HSI compressed sensing reconstruction. MAHTRGS not only fully captures the hybrid low-rank priors, gradient sparsity, and spatial-spectral smoothness characteristics of HSI, but also makes the model more succinct and efficient. Firstly, we establish a new tensor low-rank model, termed multiangle hybrid tensor rank (MAHTR). The MAHTR model can represent different high-dimensional data structures and have certain complementarities. Specifically, distinct from other hybrid rank models, MAHTR can simultaneously capture both spectral and spatial low-rank features, thoroughly exploring the hybrid low-rank properties from various perspectives. Then, taking into account that the gradient images of HSI exhibit pronounced sparse features, we devise a model to capture the sparsity of gradient images, named gradient sparsity (GS). Meanwhile, the combination of gradient maps and spatial-spectral hybrid gradient maps supplements the smooth information across the entire spatial and spectral dimensions, and leverages the global spatial-spectral correlation. Finally, we optimize the proposed model using the Alternating Direction Method of Multipliers (ADMM). Experimental results on different hyperspectral datasets demonstrate that the proposed method outperforms existing advanced methods, which proves its superiority.