A Novel Measurement Matrix Optimization Approach for Hyperspectral Unmixing

Su Xu,Xiping He

doi:10.1155/2017/8471024

Abstract

Each pixel in the hyperspectral unmixing process is modeled as a linear combination of endmembers, which can be expressed in the form of linear combinations of a number of pure spectral signatures that are known in advance. However, the limitation of Gaussian random variables on its computational complexity or sparsity affects the efficiency and accuracy. This paper proposes a novel approach for the optimization of measurement matrix in compressive sensing (CS) theory for hyperspectral unmixing. Firstly, a new Toeplitz-structured chaotic measurement matrix (TSCMM) is formed by pseudo-random chaotic elements, which can be implemented by a simple hardware; secondly, rank revealing QR factorization with eigenvalue decomposition is presented to speed up the measurement time; finally, orthogonal gradient descent method for measurement matrix optimization is used to achieve optimal incoherence. Experimental results demonstrate that the proposed approach can lead to better CS reconstruction performance with low extra computational cost in hyperspectral unmixing.

Highlights

Compressive sensing (CS) theory [1, 2] is a new developed theoretical framework on signal sampling and data compression, which indicates that if a signal is sparse or compressible in a certain transform domain, the transformed higherdimensional signal can be projected onto a lower dimensional space by a measurement matrix
Considering the D-dimensional Kronecker sparsifying basis Ψ = Ψ1 ⊗Ψ2 ⊗⋅ ⋅ ⋅⊗ΨD and a global measurement basis or frames obtained through a Kronecker product of individual measurement bases, the definition of mutual coherence is presented as μ (Φ1 ⊗ Φ2 ⊗ ⋅ ⋅ ⋅ ⊗ ΦD, Ψ1 ⊗ Ψ2 ⊗ ⋅ ⋅ ⋅ ⊗ ΨD)
Experiments on the hyperspectral data of Urban demonstrate that the proposed scheme substantially improves the reconstruction accuracy

Summary

Introduction

Compressive sensing (CS) theory [1, 2] is a new developed theoretical framework on signal sampling and data compression, which indicates that if a signal is sparse or compressible in a certain transform domain, the transformed higherdimensional signal can be projected onto a lower dimensional space by a measurement matrix. The possibility of fusing these two attractive optimized methods is certain: rank revealing QR factorization with eigenvalue decomposition from Xu et al.’s algorithm [15] and orthogonal gradient descent approach from Tian et al.’s algorithm [19] to obtain a new optimized method to overcome the computational complexity. This is my intuitive idea of this paper.

Problem Formulation and Analysis

The Proposed Approach

Experiments and Result Analysis

Findings

Conclusions