Large-Scale Hyperspectral Image Restoration via a Superpixel Distributed Algorithm Based on Graph Signal Processing

Abstract

Hyperspectral image (HSI) is often disturbed by various kinds of noise, which brings great challenges to subsequent applications. Many of the existing restoration algorithms do not scale well for HSI with large size. This paper proposes a novel mixed-noise removal method for HSI with large size, by leveraging the superpixel segmentation-based technology and distributed algorithm based on graph signal processing. First, the underlying structure of the HSI is modeled by a two-layer architecture graph. The upper layer, called skeleton graph, is a rough graph constructed by using the modified <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -nearest-neighborhood algorithm and its nodes correspond to a series of superpixels formed by HSI segmentation. The skeleton graph can efficiently characterize the inter-correlations between superpixels, while preserving the boundary information and reducing the computational complexity. The lower layer, called detailed graph consisting of a series of local graphs which are constructed to model the similarities between pixels. Second, based on the two-layer graph architecture, the HSI restoration problem is formulated as a series of optimization problems each of which resides on a subgraph. In each optimization problem, a graph Laplacian regularization is defined and incorporated into a low-rank-based model. Third, a novel distributed algorithm is tailored for the restoration problem, by using the information interaction between the nodes of skeleton graph and subgraphs. Numerical experiments conducted on both synthetic and real-world datasets demonstrate the effectiveness of the proposed restoration algorithm compared with existing methods.