Approximate Extraction of Late-Time Returns via Morphological Component Analysis

A fundamental challenge in acoustic data processing is to separate a measured time series into relevant phenomenological components. A given measurement is typically assumed to be an additive mixture of myriad signals plus noise whose separation forms an ill-posed inverse problem. In the setting of sensing elastic objects using active sonar, we wish to separate the early-time returns (e.g., returns from the object's exterior geometry) from late-time returns caused by elastic or compressional wave coupling. Under the framework of Morphological Component Analysis (MCA), we compare two separation models using the short-duration and long-duration responses as a proxy for early-time and late-time returns. Results are computed for Stanton's elastic cylinder model as well as on experimental data taken from an in-Air circular Synthetic Aperture Sonar (AirSAS) system, whose separated time series are formed into imagery. We find that MCA can be used to separate early and late-time responses in both cases without the use of time-gating. The separation process is demonstrated to be robust to noise and compatible with AirSAS image reconstruction. The best separation results are obtained with a flexible, but computationally intensive, frame based signal model, while a faster Fourier Transform based method is shown to have competitive performance.

Enveloped Sinusoid Parseval Frames

This paper presents a method of constructing Parseval frames from any collection of complex envelopes. The resulting Enveloped Sinusoid Parseval (ESP) frames can represent a wide variety of signal types as specified by their physical morphology. Since the ESP frame retains its Parseval property even when generated from a variety of envelopes, it is compatible with large scale and iterative optimization algorithms. ESP frames are constructed by applying time-shifted enveloping functions to the discrete Fourier Transform basis, and in this way are similar to the short-time Fourier Transform. This work provides examples of ESP frame generation for both synthetic and experimentally measured signals. Furthermore, the frame's compatibility with distributed sparse optimization frameworks is demonstrated, and efficient implementation details are provided. Numerical experiments on acoustics data reveal that the flexibility of this method allows it to be simultaneously competitive with the STFT in time-frequency processing and also with Prony's Method for time-constant parameter estimation, surpassing the shortcomings of each individual technique.