Random observations on random observations: Sparse signal acquisition and processing

In recent years, signal processing has come under mounting pressure to accommodate the increasingly high-dimensional raw data generated by modern sensing systems. Despite extraordinary advances in computational power, processing the signals produced in application areas such as imaging, video, remote surveillance, spectroscopy, and genomic data analysis continues to pose a tremendous challenge. Fortunately, in many cases these high-dimensional signals contain relatively little information compared to their ambient dimensionality. For example, signals can often be well-approximated as a sparse linear combination of elements from a known basis or dictionary. Traditionally, sparse models have been exploited only after acquisition, typically for tasks such as compression. Recently, however, the applications of sparsity have greatly expanded with the emergence of compressive sensing, a new approach to data acquisition that directly exploits sparsity in order to acquire analog signals more efficiently via a small set of more general, often randomized, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. A common theme in this research is the use of randomness in signal acquisition, inspiring the design of hardware systems that directly implement random measurement protocols. This thesis builds on the field of compressive sensing and illustrates how sparsity can be exploited to design efficient signal processing algorithms at all stages of the information processing pipeline, with a particular focus on the manner in which randomness can be exploited to design new kinds of acquisition systems for sparse signals. Our key contributions include: (i) exploration and analysis of the appropriate properties for a sparse signal acquisition system; (ii) insight into the useful properties of random measurement schemes; (iii) analysis of an important family of algorithms for recovering sparse signals from random measurements; (iv) exploration of the impact of noise, both structured and unstructured, in the context of random measurements; and (v) algorithms that process random measurements to directly extract higher-level information or solve inference problems without resorting to full-scale signal recovery, reducing both the cost of signal acquisition and the complexity of the post-acquisition processing.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Engineering

Grantor

Rice University

Year dc:date.issued

2010

Author dc:creator

• Davenport, Mark A.

Advisor dc:contributor.advisor

• Baraniuk, Richard G.

• Applied mechanics
• Statistics
• Electronics
• Electrical engineering

Statement dc:rights

• Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/62225

OAI identifier oai:identifier

oai:repository.rice.edu:1911/62225