Piecewise Weighted Smoothing Regularization in Tight Framelet Domain for Hyperspectral Image Restoration

Abstract

Hyperspectral images captured by remote-sensing satellites are easily corrupted by various types of noise. Generally, hyperspectral signatures appear to be scattered in spatial-spectral domain, as well as noise. In transform domain, however, the principal components of a image are often centralized in the low-frequency band, while noise and some details are mainly contained in high-frequency components. The traditional transformation domain based smoothing methods take no account of the respective information distribution carried by different frequency bands. Hyperspectral image restoration aims to remove mixed noise for clean data, which usually amounts to an ill-posed inverse problem. Moreover, the matrix-decomposition-based model needs to reshape hyperspectral datacube into matrix form, which will lead to certain loss of spatial structure information. In order to address these issues, this paper incorporates piecewise weighted smoothing regularization in tight framelet domain to reformulate a novel convex model for hyperspectal image restoration, which maintains image signature to a great extent. Based on the noise-perturbed degradation model, the smoothing regularizer in tight framelet domain is imposed on abundance signature, in which the transformation matrix, as well as the weighted coefficient, is well designed for different frequency bands. As a surrogate of sparsity, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{q}$ </tex-math></inline-formula> -norm is employed to denoise for the enhancement of hyperspectral signatures. To the end, an efficient solver is carefully designed to derive the closed-form solutions by proximal alternating optimization. The experimental results on several synthetic and real datasets, not only demonstrate that the performance of proposed method is better than that of the current state-of-the-art approaches, but also verify the validation of regularization terms for hyperspectral image restoration.