Book chapter
Sampling at the rate of innovation: theory and applications
Compressed Sensing:Theory and Applications, pp.148-209
2012
Abstract
Parametric signals, such as streams of short pulses, appear in many applications including bio-imaging, radar, and spread-spectrum communication. The recently developed finite rate of innovation (FRI) framework has paved the way to low-rate sampling of such signals, by exploiting the fact that only a small number of parameters per unit of time are needed to fully describe them. For example, a stream of pulses can be uniquely defined by the time delays of the pulses and their amplitudes, which leads to far fewer degrees of freedom than the signal's Nyquist rate samples. This chapter provides an overview of FRI theory, algorithms, and applications. We begin by discussing theoretical results and practical algorithms allowing perfect reconstruction of FRI signals from a minimal number of samples. We then turn to treat recovery from noisy measurements. Finally, we overview a diverse set of applications of FRI theory, in areas such as super-resolution, radar, and ultrasound.<br/><br/>Introduction We live in an analog world, but we would like our digital computers to interact with it. For example, sound is a continuous-time phenomenon, which can be characterized by the variations in air pressure as a function of time. For digital processing of such real-world signals to be possible, we require a sampling mechanism which converts continuous signals to discrete sequences of numbers, while preserving the information present in those signals.In classical sampling theory, which dates back to the beginning of the twentieth century [1–3], a bandlimited signal whose maximum frequency is fmax is sampled at or above the Nyquist rate 2fmax.
Details
- Title
- Sampling at the rate of innovation; theory and applications
- Creators
- Jose Antonio Urigüen (null) - Imperial College LondonYonina C. Eldar (null) - Technion – Israel Institute of TechnologyPier Luigi Dragotti (null) - Imperial College LondonZvika Ben-Haim (null) - Technion – Israel Institute of Technology
- Resource Type
- Book chapter
- Publication Details
- Compressed Sensing:Theory and Applications, pp.148-209; 2012
- Chapter Number
- Book Chapter: 4
- Number of pages
- 62
- Book Editors
- Eldar, Yonina C. ; Kutyniok, Gitta
- Publisher
- Cambridge University Press
- Language
- English
- DOI
- https://doi.org/10.1017/CBO9780511794308.005
- Grant note
- Y. Eldar would like to thank Kfir Gedalyahu for many helpful comments.
- ISBN
- 9781107005587
- Record Identifier
- 993267853303596
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