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 l_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.

I. Introduction

In scientific, medical, remote sensing and other technical fields, many vision tasks, such as segmentation [1], tracking [2], classification [3], recognition [4], [5], etc., require both high spatial resolution and high spectral fidelity of input images [6]–[9]. For instances, in environment studies, in order to discriminate different types of vegetation that are closely and intricately mingled on earth surface, measure and track their growths, remote sensing images must offer high precision in both spectral and spatial domains; such is also the case in urban planning and administration for accurate classification and measurement of man-made and natural objects using multispectral images. The same is true in quantitative medical diagnosis, such as accurate identification, segmentation and assessment of skin lesions based on dermatology images. Even for imaging products and services in consumer applications, the thrust of technology development is shifting from high spatial resolution to high color quality. Indeed, nowadays many optical image acquisition and display devices push color reproduction fidelity to the limit of human vision.