Multispectral Image Super-Resolution with $\ell_{1,2}$-Norm Regularization of Spatially-Aligned Laplacians

In quest for high spectral fidelity in spatial superresolution of multispectral images, we explore physically-induced, joint spectral-spatial sparsities. The bichromatic image formation model is used to reveal that the discontinuities of a multispectral image tend to align spatially across different spectral bands; in other words, the 2D Laplacians of different bands are not only sparse but also agree with one the other in positions of significance. This strong prior of natural images can be incorporated, as an $\ell_{1,2}$-norm regularization term, into an inverse problem formulation for superresolution of multispectral images. Experiments show that exploiting the newly discovered joint spectral-spatial sparsities can improve the performance of existing methods, especially in spectral fidelity.