Compressive spectral imaging (SI) (CSI) acquires few random projections of an SI reducing acquisition, storage, and, in some cases, processing costs. Then, this acquisition framework has been widely used in various tasks, such as target detection, video processing, and fusion. Particularly, compressive spectral image fusion (CSIF) aims at obtaining a high spatial-spectral resolution SI from two sets of compressed measurements: one from a hyperspectral image with a high-spectral low-spatial resolution, and one from a multispectral image with high-spatial low-spectral resolution. Most of the literature approaches include prior information, such as global low rank, smoothness, and sparsity, to solve the resulting ill-posed CSIF inverse problem. More recently, the high self-similarities exhibited by SIs have been successfully used to improve the performance of CSI inverse problems, including a nonlocal low-rank …