Hyperspectral Unmixing with Robust Collaborative Sparse Regression

Chang Li,Jiayi Ma,Yong Ma,Chengyin Liu,Xiaoguang Mei

doi:10.3390/rs8070588

Abstract

Recently, sparse unmixing (SU) of hyperspectral data has received particular attention for analyzing remote sensing images. However, most SU methods are based on the commonly admitted linear mixing model (LMM), which ignores the possible nonlinear effects (i.e., nonlinearity). In this paper, we propose a new method named robust collaborative sparse regression (RCSR) based on the robust LMM (rLMM) for hyperspectral unmixing. The rLMM takes the nonlinearity into consideration, and the nonlinearity is merely treated as outlier, which has the underlying sparse property. The RCSR simultaneously takes the collaborative sparse property of the abundance and sparsely distributed additive property of the outlier into consideration, which can be formed as a robust joint sparse regression problem. The inexact augmented Lagrangian method (IALM) is used to optimize the proposed RCSR. The qualitative and quantitative experiments on synthetic datasets and real hyperspectral images demonstrate that the proposed RCSR is efficient for solving the hyperspectral SU problem compared with the other four state-of-the-art algorithms.

Highlights

Over the last few decades, hyperspectral imaging (HSI) has been receiving considerable attention in different remote sensing applications such as spectral unmixing, object classification and matching [1,2,3,4,5]
We use the spectral library randomly selected from the United States Geological Survey (USGS) digital spectral library (Available at: http://speclab.cr.usgs.gov/spectral-lib.html), which has spectral bands uniformly ranging from 0.4 μm to 2.5 μm, and contains 498 spectral signatures of endmembers
We generate the synthetic HSI based on the linear mixing model (LMM) [16], Fan bilinear model (FM) [23], generalized bilinear model (GBM) [24] and modified GBM (MGBM) [25], and the latter three models are nonlinear unmixing models

Summary

Introduction

Over the last few decades, hyperspectral imaging (HSI) has been receiving considerable attention in different remote sensing applications such as spectral unmixing, object classification and matching [1,2,3,4,5]. Spectral unmixing is an essential step for the deep exploitation of hyperspectral image, which decomposes mixed pixels into a collection of pure spectra signatures, called endmembers, and their corresponding proportions in each pixel, called abundances [9,10]. Sparse unmixing (SU) assumes that the observed image can be formulated as finding the optimal subset of pure spectral signatures from a prior large spectral library, and it can typically be formulated as a linear sparse regression problem. To solve this problem, Bioucas et al proposed sparse unmixing by variable splitting and augmented Lagrangian (SUnSAL) [14], which ignores

Methods

Results

Conclusion