Data-driven morphological component analysis

Abstract

A common goal in signal processing is to decompose a signal into constituent components. Morphological Component Analysis (MCA) is a convex optimization technique that can be used to decompose a signal into a sum of sparse representations determined by chosen dictionaries. Previously, MCA has been shown to successfully decompose sonar data into long-duration and short duration components, using Enveloped Sinusoid Parseval (ESP) frames as the dictionaries. However, in its current state, ESP MCA is model-driven and requires prior selection of envelope parameters. This presentation describes the addition of hyper-parameter tuning to ESP MCA. Specifically, gradient descent is performed on an unrolled version of the ESP MCA regularization algorithm in order to learn the optimal envelope parameters used to construct the ESP frames. Addition of hyper-parameter tuning allows the dictionary atoms to adapt and thus improves sparse representation of the sensed data.