Hyperspectral-Multispectral Image Fusion with Rank Estimation by using a Joint-sparse Regularizer

Combining information of a low-spatial resolution hyperspectral image (HSI) and a low-spectral resolution multispectral image (MSI) to obtain a high spatial-spectral resolution image (HRI) has become an important framework for some applications such as remote sensing. The state-of-the-art approaches use the prior information of the HRI, as sparsity, smoothness, or low-rankness, to solve the resultant fusion inverse problem. However, these methods using a global low-rank commonly require to know a priori the rank of the HRI, which is hardly ever known in the acquisition process. Therefore, this work introduces a joint-sparse regularizer in order to estimate the rank of the HRI intrinsically. Specifically, the proposed method follows an alternating direction method of multipliers based on the linear mixture decomposition. Simulations showed that the proposal allows fusing the HSI and MSI source while estimating the rank of the HRI during the iterative process.