Recovery of sparse signals and parameter perturbations from parameterized signal models

Estimating unknown signals from parameterized measurement models is a common problem that arises in diverse areas such as statistics, imaging, machine learning, and signal processing. In many of these problems, however, only a limited amount of data is available to recover the unknown signal. Additional constraints are required to successfully recover the unknown signal if there are more unknowns than measurements. Sparsity has proven to be a powerful constraint for signal recovery when the unknown signal has few nonzero elements. If a signal is sparse in a parameterized measurement model, the model parameters must be known to recover the signal. An example of this problem is the recovery of a signal that is a sum of a small number of sinusoids. Reconstruction of this signal requires recovery of both the amplitude of the sinusoids as well as their frequency parameters. Applying traditional sparse reconstruction techniques to such problems requires a dense oversampling of the parameter space. As an alternative to existing methods, this work proposes an optimization problem to recover sparse signals and sparse parameter perturbations from few measurements given a parameterized model and an initial set of parameter estimates. This problem is then solved by a newly developed Successive Linearized Programming for Sparse Representations algorithm, which is guaranteed to converge to a first-order critical point. For simulated recovery of four sinusoids from 16 noiseless measurements, this method is able to perfectly recover the signal amplitudes and parameters whereas existing approaches have signi cant error. To demonstrate the potential application of the proposed technique to real-world problems, the novel algorithm is used to fi nd sparse representations of real-world Radio Frequency data. With this dataset, the proposed technique is able to produce sparse recoveries without highly oversampled dictionaries and actually produces sparser solutions than standard sparse recovery techniques with oversampled dictionaries.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Johnson, Erik C.

Contributors dc:contributor

• Jones, Douglas L.

• Sparse Recovery
• Compressed Sensing
• Sparse Signal
• Parameterized Model
• Dictionary Perturbation

Statement dc:rights

• Copyright 2013 Erik C. Johnson

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/44187

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/44187