Hyperspectral image restoration by Hybrid Spatio-Spectral Total Variation

Abstract

We propose a new regularization technique, named Hybrid Spatio-Spectral Total Variation (HSSTV), for hyperspectral image (HSI) restoration. Popular regularization techniques for HSIs are total variation functions (TV), and there have been proposed a variety of TVs for HSI restoration. However, they do not fully exploit both spatial and spectral smoothness, which are the underlying properties of HSIs, and/or they result in computationally expensive optimization. Our proposed HSSTV is designed to evaluate the two properties via two types of discrete differences of an HSI, leading to much more effective regularization than existing TVs for HSI restoration. HSSTV is defined with local discrete difference operators and the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> /mixed ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1,2</sub> norm, so that optimization problems involving it can be efficiently solved by proximal splitting methods, such as the so-called alternating direction method of multipliers. Experimental results illustrate the advantages of HSSTV over state-of-the-art methods.