Pansharpening via semi-framelet-guided sparse reconstruction

Pansharpening involves the spatial super-resolution of a low-resolution multispectral (LR-MS) image by leveraging a simultaneously acquired panchromatic (PAN) image, aiming to generate a high-resolution multispectral (HR-MS) image. Such an inverse problem mainly requires more accurately establishing the relation between the underlying HR-MS image and the PAN image. Because of the high redundancy of framelet transform, the framelet-based sparse error reconstruction has recently been well-investigated and achieved promising results. Nevertheless, previous works ignore the negative impact of the low-pass filter within the framelet, which experimentally distinguishes the coefficient similarity and reduces the error sparsity, thereby leading to limited numerical performance and high hyperparameter sensitivity. In this paper, we propose an improved pansharpening model via semi-framelet-guided sparse reconstruction, called SemiFGSR. This model only considers the partial rather than the whole framelet transform, which avoids the interference of low-frequency information, thus facilitating sparse reconstruction. To solve the proposed norm-based model, we develop an efficient proximal alternating minimization (PAM)-based algorithm and theoretically prove its convergence. Numerical experiments conducted on various datasets demonstrate the superiority of the SemiFGSR, revealing the effectiveness of such semi-framelet-guided improvement.