Abstract
The proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set. This tool plays a central role in the analysis and the numerical solution of convex optimization problems. It has recently been introduced in the area of signal processing, where it has become increasingly important. However, so far there has been no research on independent component analysis (ICA) in this framework. In this paper, we focus on this problem and propose the fast proximal-gradient method for ICA, termed as FastPG-ICA, in blind source separation (BSS) problem. We derive the new update rule of the unmixing matrix from the viewpoint of the fast proximal gradient. It achieves a better separation performance than that of the traditional ICA method, such as complex FastICA (cFastICA) proposed by Bingham and Hyvarinen. Simulations demonstrate the effectiveness of our proposed method.
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