Blind source separation by convex optimization to resolution enhancement
Kenbu Teramoto, Noriko Mori · The Journal of the Acoustical Society of America · 1999
In the current blind source separation (BSS) one tries to separate statistically independent unknown source signals from their linear mixtures without explicit knowledge of the mixing coefficients. However, in the case that the sources radiate statistically dependent signals, difficulties exist in separating sources. In such cases, it is important to utilize the nonlinear convex constraints. In this paper, a convex optimization method for BSS and parameter estimation of unknown components in the signal transfer function is proposed. This technique relies upon seeking the unique KKT (Karush–Kuhn–Tucker) point of the augmented Lagrange function which is defined over the direct product of source object space and observed signal space. Utilizing prior knowledge about spatial characteristics of the point spread function and short-time statistical characteristics of noise concurrently, the proposed algorithm can converge to the reliable solution on the contrary to the independent component analysis (ICA) exhibiting oscillations. Applying the proposed method to a 3-D sparse aperture holographic sonar which has a limited number of transducers distributed sparsely, the novel method yields features that reduce the artifacts caused by under-sampled data and achieve higher resolution with higher convergence rate to the optimal solution than that of ICA.