Sparse and low-rank abundance estimation with structural information

Abundance estimation (AE) plays an essential role in the hyperspectral image processing and analysis. Owing to the simplicity and mathematical tractability, various methods based on the constrained linear regression are usually developed to estimate abundance matrix. The obvious limitation of these approaches is that the fitness between the estimated data and ground-truth data does not include the structural information, e.g. row difference and column difference. In this paper, a novel linear regression algorithm is proposed by jointly adding the multi structured information to the traditional linear regression model. And it is employed to modify sparse and low-rank abundance estimation model to improve estimated accuracy and robustness. Firstly, a new linear regression model is established by taking into account the structural information. Then, mathematical proof of the new linear regression method is presented. Afterwards, it is 'applied to modify the sparse low-rank abundance estimation model. Finally, Alternating Direction Method of Multipliers (ADMM) technique is adopted to solve the new model. The experimental results demonstrate that the proposed algorithms can capture structural information and improve the estimated performance on the simulated dataset and the real hyperspectral remote sensing images.