Optimal dictionary learning with application to underwater target detection from synthetic aperture sonar imagery

Abstract

K-SVD is a relatively new method used to create a dictionary matrix that best ts a set of training data vectors formed with the intent of using it for sparse representation of a data vector. K-SVD is flexible in that it can be used in conjunction with any preferred pursuit method of sparse coding including the orthogonal matching pursuit (OMP) method considered in this thesis. Using adaptive lter theory, a new fast OMP method has been proposed to reduce the computational time of the sparse pursuit phase of K-SVD as well as during on-line implementation without sacrificing the accuracy of the sparse pursuit method. Due to the matrix inversion required in the standard OMP, the amount of time required to sparsely represent a signal grows quickly as the sparsity restriction is relaxed. The speed up in the proposed method was accomplished by replacing this computationally demanding matrix inversion with a series of recursive "time-order" update equations by using orthogonal projection updating used in adaptive filter theory. The geometric perspective of this new learning is also provided. Additionally, a recursive method for faster dictionary learning is also discussed which can be used instead of the singular value decomposition (SVD) process in the K-SVD method. A significant bottleneck in K-SVD is the computation of the SVD of the reduced error matrix during the update of each dictionary atom. The SVD operation is replaced with an efficient recursive update which will allow limited in-situ learning to update dictionaries as the system is exposed to new signals. Further, structured data formatting has allowed a multi-channel extension of K-SVD to merge multiple data sources into a single dictionary capable of creating a single sparse vector representing a variety of multi-channel data. Another contribution of this work is the application of the developed methods to an underwater target detection problem using coregistered dual-channel (namely broadband and high-frequency) side-scan sonar imagery data. Here, K-SVD is used to create a more optimal dictionary in the sense of reconstructing target and non-target image snippets using their respective dictionaries. The ratio of the reconstruction errors is used as a likelihood ratio for target detection. The proposed methods were then applied and benchmarked against other detection methods for detecting mine-like objects from two dual-channel sonar datasets. Comparison of the results in terms of receiver operating characteristic (ROC) curve indicates that the dual-channel K-SVD based detector provides a detection rate of PD = 99% and false alarms rate of PFA = 1% on the first dataset, and PD = 95% and PFA = 5% on the second dataset at the knee point of the ROC. The single-channel K-SVD based detector on the other hand, provides PD = 96% and PFA = 4% on the first dataset, and PD = 96% and PFA = 4% on the second dataset at the knee point of the ROC. The degradation in performance for the second dataset is attributed to the fact that the system was trained on a limited number of samples from the first dataset. The coherence-based detector provides PD = 87% and PFA = 13% on the first dataset and PD = 86% and PFA = 14% on the second dataset. These results show excellent performance of the proposed dictionary learning and sparse coding methods for underwater target detection using both dual-channel sonar imagery.