Walter Scott, Jr. College of Engineering

Graduate Exam Abstract

Justin Kopacz
M.S. Final
Mar 26, 2014, 2:00pm to 3:30pm
Titan Studio, ENGRG B203
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 fits a set of training data vectors. This dictionary is 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. This includes the orthogonal
matching pursuit (OMP) method considered in this thesis. A new fast OMP
method has been proposed to reduce the computation 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 new 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 is replaced
with an efficient recursive update which allows limited in-situ learning
to update dictionaries as the system is exposed to new signals.
Further, structured data formatting has allowed a multi-modal 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. Results show superiority of the proposed dictionary learning
and sparse coding methods for underwater target detection using dual-
channel sonar imagery.
Adviser: Mahmood R. Azimi-Sadjadi
Co-Adviser: N/A
Non-ECE Member: Jay Breidt, Statistics
Member 3: Ali Pezeshki, ECE
Addional Members: N/A
M. R. Azimi-Sadjadi, J. Kopacz, and N. Klausner, "K-SVD Dictionary Learning Using A Fast OMP With Applications", Submitted to IEEE Conference on Signal Processing.
Program of Study: