Constrained signal reconstruction

The research reported in this dissertation addresses the reconstruction of signals and images from linear measurements subject to convex constraints. The objectives are to describe the existence and uniqueness of solutions, to characterize reconstructions, and to develop algorithms for efficiently computing reconstructions. A prototypical inverse problem of this type is the extrapolation of a positive semidefinite sequence, which is equivalent to the covariance extension and trigonometric moment problems. Classical results are extended to incorporate the additional convex constraints imposed by spectral support limits and bounding functions. An order N$\sp2$ matrix test is given for the extendibility of a partial covariance sequence subject to a spectral support constraint, and recursive reconstruction algorithms employing the Levinson algorithm follow from the constructive proof.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Potter, Lee Carson

Contributors dc:contributor

• Arun, K.S.

• Engineering, Electronics and Electrical

Statement dc:rights

• Copyright 1990 Potter, Lee Carson

Language dc:language

eng

Identifier

AAI9114377
(UMI)AAI9114377

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/19116