4 research outputs found
Using the Eigenvalue Relaxation for Binary Least-Squares Estimation Problems
The goal of this paper is to survey the properties of the eigenvalue
relaxation for least squares binary problems. This relaxation is a convex
program which is obtained as the Lagrangian dual of the original problem with
an implicit compact constraint and as such, is a convex problem with polynomial
time complexity. Moreover, as a main pratical advantage of this relaxation over
the standard Semi-Definite Programming approach, several efficient bundle
methods are available for this problem allowing to address problems of very
large dimension. The necessary tools from convex analysis are recalled and
shown at work for handling the problem of exactness of this relaxation. Two
applications are described. The first one is the problem of binary image
reconstruction and the second is the problem of multiuser detection in CDMA
systems
A Linear Algebraic Framework for Autofocus in Synthetic Aperture Radar
Synthetic aperture radar (SAR) provides a means of producing high-resolution microwave
images using an antenna of small size. SAR images have wide applications
in surveillance, remote sensing, and mapping of the surfaces of both the Earth and
other planets. The defining characteristic of SAR is its coherent processing of data
collected by an antenna at locations along a trajectory in space. In principle, we can
produce an image of extraordinary resolution. However, imprecise position measurements
associated with data collected at each location cause phase errors that, in turn,
cause the reconstructed image to suffer distortion, sometimes so severe that the image
is completely unrecognizable. Autofocus algorithms apply signal processing techniques
to restore the focused image.
This thesis focuses on the study of the SAR autofocus problem from a linear algebraic
perspective. We first propose a general autofocus algorithm, called Fourier-domain
Multichannel Autofocus (FMCA), that is developed based on an image support
constraint. FMCA can accommodate nearly any SAR imaging scenario, whether
it be wide-angle or bistatic (transmit and receive antennas at separate locations). The
performance of FMCA is shown to be superior compared to current state-of-the-art
autofocus techniques.
Next, we recognize that at the heart of many autofocus algorithms is an optimization
problem, referred to as a constant modulus quadratic program (CMQP). Currently,
CMQP generally is solved by using an eigenvalue relaxation approach. We propose an
alternative relaxation approach based on semidefinite programming, which has recently
attracted considerable attention in other signal processing applications. Preliminary
results show that the new method provides promising performance advantages at the
expense of increasing computational cost.
Lastly, we propose a novel autofocus algorithm based on maximum likelihood estimation,
called maximum likelihood autofocus (MLA). The main advantage of MLA is
its reliance on a rigorous statistical model rather than on somewhat heuristic reverse engineering
arguments. We show both the analytical and experimental advantages of
MLA over existing autofocus methods.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86443/1/khliu_1.pd