Decomposition of Higher-Order Spectra for Blind Multiple-Input Deconvolution, Pattern Identification and Separation

TL;DR

This paper introduces a novel higher-order spectra decomposition technique for blind multi-input deconvolution, enabling waveform identification and separation without prior information, suitable for real-time signal processing applications.

Contribution

The paper presents a new HOS-based method for blind deconvolution that works with deterministic and non-deterministic signals, improving upon MED by avoiding optimization.

Findings

Achieves near-optimal waveform detection performance.

Effective separation of non-Gaussian signal components.

Demonstrated successful application to ECG heartbeat classification.

Abstract

Like the ordinary power spectrum, higher-order spectra (HOS) describe signal properties that are invariant under translations in time. Unlike the power spectrum, HOS retain phase information from which details of the signal waveform can be recovered. Here we consider the problem of identifying multiple unknown transient waveforms which recur within an ensemble of records at mutually random delays. We develop a new technique for recovering filters from HOS whose performance in waveform detection approaches that of an optimal matched filter, requiring no prior information about the waveforms. Unlike previous techniques of signal identification through HOS, the method applies equally well to signals with deterministic and non-deterministic HOS. In the non-deterministic case, it yields an additive decomposition, introducing a new approach to the separation of component processes within non-Gaussian signals having non-deterministic higher moments. We show a close relationship to minimum-entropy blind deconvolution (MED), which the present technique improves upon by avoiding the need for numerical optimization, while requiring only numerically stable operations of time shift, element-wise multiplication and averaging, making it particularly suited for real-time applications. The application of HOS decomposition to real-world signals is demonstrated with blind denoising, detection and classification of normal and abnormal heartbeats in electrocardiograms.