Exploiting Low-Rank and Sparse Properties in Strided Convolution Matrix for Pansharpening

Fusion of low spatial resolution multispectral (LR MS) and panchromatic (PAN) images to acquire high spatial resolution multispectral (HR MS) images has attracted increasing attention in recent years. In this article, we first utilize the form of convolution matrix (CM) to formulate the image fusion problem. In order to reduce the complexity of CM, the step size is introduced and strided convolution matrix (SCM) is constructed. Then, we explore the low-rank property in SCM and impose the prior on the spatial and spectral degradation model of LR MS and PAN images. Meanwhile, sparsity in SCM is considered to further enhance the local structures in the fused image. Finally, the proposed model is optimized efficiently by the alternative direction method of multipliers. By exploiting the low-rank and sparse priors in SCM of HR MS image, the local and global structures can be better preserved. The experimental results on the reduced-resolution and full-resolution datasets also show that the proposed method behaves well in qualitative and quantitative assessments.