Multispectral Image Restoration via Inter- and Intra-Block Sparse Estimation Based on Physically-Induced Joint Spatiospectral Structures
Existing low-level vision algorithms (e.g., those for superresolution, denoising, and deblurring) were primarily motivated and optimized for precision in spatial domain. However, high precision in spectral domain is of importance for many applications in scientific and technical fields, such as spectral analysis, recognition, and classification. In quest for both high spectral and spatial fidelity, we introduce previously unexplored, physically induced, and joint spatiospectral sparsities to improve existing methods for multispectral image restoration. The bidirectional 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 each, but they also agree with one the other in significance positions. Such strongly structured sparsities give rise to a new inter- and intra-block sparse estimation approach. The estimation is performed on 3D spatiospectral sample blocks, rather than on separate 2D patches, per spectral band or per luminance and chrominance component as in current practice. Moreover, intra-block and inter-block sparsity priors are combined via an intra-block  $\ell _{1,2}$ -norm minimization term and an inter-block low-rank term, strengthening the regularization of the underlying inverse problem. The new approach is tested and evaluated on two concrete applications. The superresolving and denoising multispectral images; its validity and advantages over the current state-of-the-art are established by empirical results.