A Convex Geometry-Based Blind Source Separation Method for Separating Nonnegative Sources

Abstract

This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method.

Hyperspectral Blind Unmixing Using a Double Deep Image Prior

“…where, L EDIP , L ADIP , L BU are defined in (17), (19) and (21). From the perspective of unmixing, the terms L EDIP and L ADIP in the composite loss function ensure that the network produces meaningful endmembers and abundances, in the sense that Ê, Â cannot deviate too much from E G , A G .…”

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