Blind Source Separation and Blind Mixture Identification Methods

Abstract

Blind source separation (BSS) is a generic signal processing problem. BSS methods aim to estimate a set of unknown source signals, by using a set of available signals that are mixtures of the source signals to be restored, with limited or no knowledge of the mixing transform (i.e., the transform of source signals that yields their mixtures). BSS methods were introduced in the 1980s and then quickly expanded. Various books provide a detailed description of BSS methods, or at least of some classes of such methods defined hereafter, such as independent component analysis, sparse component analysis, and nonnegative matrix factorization. Moreover, the BSS problem, focused on signal restoration, is closely linked to the estimation of the mixing transform, and thus to the problem often referred to as blind mixture identification (BMI). In this article, we overview the fields of BSS and BMI. We first define in more detail the considered goal (Section 1) and conditions of investigation (Section 2), and then we introduce the major classes of methods that make it possible to solve the considered problems. The presentation of BSS/BMI methods themselves and of typical applications is given in successive sections (Sections 3–7), where we progress from standard to more advanced configurations, in terms of properties of source signals and class of mixing transform.

Using a Panchromatic Image to Improve Hyperspectral Unmixing

“…The resulting mean criterion values, given in Table 4, show an improvement of the normalized difference by 51% in SAM ( 3.9−1. 9 3.9 × 100), 85% in SID, 55% in RMSE, and 48% in NRMSE using HBEE-LCNMF compared to the best state-of-the-art method (VCA).…”

“…Observation Asphalt To make the material identification possible, a blind source separation strategy [9] is applied to retrieve the pure material spectral signatures, i.e., the endmembers, and their relative abundance fractions in each pixel of a hyperspectral image. This problem has been widely studied for decades and is called hyperspectral unmixing in the remote sensing community.…”

A second-order statistics method for blind source separation in post-nonlinear mixtures

“…If there is no (or incomplete) prior knowledge about the sources and mixing transform, the problem is referred to as Blind Source Separation (BSS) [1,2,3]. 5 Throughout three decades of existence, this problem has been subject of great attention from the academic community, where the initial efforts were mainly aimed at the standard linear and instantaneous mixing model, with the assumption that the sources are statistically mutually independent.…”

Partial Linear NMF-Based Unmixing Methods for Detection and Area Estimation of Photovoltaic Panels in Urban Hyperspectral Remote Sensing Data

“…It should be noted that LSU methods, which can be viewed as typical linear blind source separation (BSS) approaches [8,9], are the most employed methods for processing hyperspectral remote sensing images. This process aims at linearly unmixing all observed spectra into a set of pure material spectra, and a collection of associated abundance fractions [10].…”