Morphological Component Analysis of SAS Imagery

Morphological Component Analysis of SAS Imagery Project Summary / AbstractOne of the fundamental challenges in acoustics is the sepa,ration of a time series which is a superposition of myriad signals combined with noise into relevant components. In this project we,seek to separate the active sonar return from an elastic object into an early-time component associated with the object's geometry a,nd late-time acoustic returns caused by resonant and/or elastic effects. Various methods of separating early-time and late-time retu,rns are possible, from simple time gating to subtracting the response of a rigid object from an elastic one with an identical geomet,ry. For this project we will utilize Morphological Component Analysis (MCA) to tackle this problem. MCA is a relatively new approach, based on sparse representation via L1-regularization which seeks to separate a signal into multiple components based on the ability, of each component to be sparsely encoded by an appropriately chosen representation [Selesnick, 2010].The effectiveness of MCA as an, analysis tool is entirely dependent upon the ability to sparsely represent the relevant components. This effort will utilize a rece,ntly developed set of representations called Enveloped Sinusoid Parseval (ESP) frames which are well suited for MCA. ESP frames are,formed from enveloped and shifted sinusoids and this effort will utilize envelopes informed by the physics of the associated acousti,cs.The project will apply ESP frame MCA to acoustic data drawn from three primary sources. First, the Stanton elastic cylinder model, will be used to generate analytic time series for development and evaluation of MCA signal separation in the ideal setting. Next, A,RL/PSU has developed an in-air Synthetic Aperture Sonar (SAS) data collection framework. This framework allows for the collection o,f low noise in-air SAS data. We will apply the ESP MCA approach to separate the early-time and late-time returns for a collection o,f cylindrical objects of various configurations (thin-walled copper cylinders, aluminum pipes, etc.). Finally ESP MCA will be appli,ed to underwater SAS datasets to evaluate its effectiveness in real-world applications. For each of these data sets the project will, analyze which envelopes produce the best early-time/late-time separation and what regularization parameters are optimal for a given, setting. Early-time envelopes can range from very short windowed sinusoids to pulse replicas, while late-time envelopes are often,exponentially decaying functions. Regularization parameters include weights which control prioritization of the separated component,s, potentially at the level of individual frequencies, as well as the prioritization of reconstruction fidelity over noise removal.,While the regularization parameters are currently set a priori, this effort will also investigate allowing the ESP frame parameters,to adapt as part of the regularization process to be more data informed. This makes the corresponding o,owever, and will require substantial effort. Lastly, there are numerous examples of sparse regularization in other fields which may,be applied to SAS. The project will explore the applicability of these examples, as well as alternative regularization approaches, s,uch as Overlapping Group Sparsity and Total Variation, to the study of sonar data. The effort will also consider the use of sparsif,ied or separated signal components in traditional SAS applications such as imaging, feature detection and feature classification. DI,STRIBUTION STATEMENT A. Approved for public release. Distribution is unlimited.