Self-Dictionary Sparse Regression for Hyperspectral Unmixing: Greedy Pursuit and Pure Pixel Search are Related

This paper considers a recently emerged hyperspectral unmixing formulation based on sparse regression of a self-dictionary multiple measurement vector (SD-MMV) model, wherein the measured hyperspectral pixels are used as the dictionary. Operating under the pure pixel assumption, this SD-MMV formalism is special in that it allows simultaneous identification of the endmember spectral signatures and the number of endmembers. Previous SD-MMV studies mainly focus on convex relaxations. In this study, we explore the alternative of greedy pursuit, which generally provides efficient and simple algorithms. In particular, we design a greedy SD-MMV algorithm using simultaneous orthogonal matching pursuit. Intriguingly, the proposed greedy algorithm is shown to be closely related to some existing pure pixel search algorithms, especially, the successive projection algorithm (SPA). Thus, a link between SD-MMV and pure pixel search is revealed. We then perform exact recovery analyses, and prove that the proposed greedy algorithm is robust to noise---including its identification of the (unknown) number of endmembers---under a sufficiently low noise level. The identification performance of the proposed greedy algorithm is demonstrated through both synthetic and real-data experiments

SPATIAL-SPECTRAL UNMIXING OF HYPERSPECTRAL DATA FOR DETECTION AND ANALYSIS OF ASTROPHYSICAL SOURCES WITH THE MUSE INSTRUMENT

International audienceDetection and analysis of astrophysical sources from the forthcoming MUSE instrument is of greatest challenge mainly due to the high noise level and the three-dimensional translation variant blur effect of MUSE data. In this work, we use some realistic hypotheses of MUSE to reformulate the data convolution model into a set of linear mixing models corresponding to different, disjoint spectral frames. Based on the linear mixing models, we propose a spatial-spectral unmixing (SSU) algorithm to detect and characterize the galaxy spectra. In each spectral frame, the SSU algorithm identifies the pure galaxy regions with a theoretical guarantee, and estimate spectra based on a sparse approximation assumption. The full galaxy spectra can finally be recovered by concatenating the spectra estimates associated with all the spectral frames. The simulations were performed to demonstrate the efficacy of the proposed SSU algorithm

A convex analysis based criterion for blind separation of non-negative sources

[[abstract]]In this paper, we apply convex analysis to the problem of blind source separation (BSS) of non-negative signals. Under realistic assumptions applicable to many real-world problems such as multichannel biomedical imaging, we formulate a new BSS criterion that does not require statistical source independence, a fundamental assumption to many existing BSS approaches. The new criterion guarantees perfect separation (in the absence of noise), by constructing a convex set from the observations and then finding the extreme points of the convex set. Some experimental results are provided to demonstrate the efficacy of the proposed method. © 2007 IEEE.[[fileno]]2030157030001[[department]]電機工程學