Sensing by Random Convolution (2007)
| Venue: | IEEE Int. Work. on Comp. Adv. Multi-Sensor Adaptive Proc., CAMPSAP |
| Citations: | 37 - 2 self |
BibTeX
@ARTICLE{Romberg07sensingby,
author = {Justin Romberg},
title = {Sensing by Random Convolution},
journal = {IEEE Int. Work. on Comp. Adv. Multi-Sensor Adaptive Proc., CAMPSAP},
year = {2007},
pages = {137--140}
}
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Abstract
Abstract. This paper outlines a new framework for compressive sensing: convolution with a random waveform followed by random time domain subsampling. We show that sensing by random convolution is a universally efficient data acquisition strategy in that an n-dimensional signal which is S sparse in any fixed representation can be recovered from m � S log n measurements. We discuss two imaging scenarios — radar and Fourier optics — where convolution with a random pulse allows us to seemingly super-resolve fine-scale features, allowing us to recover high-resolution signals from low-resolution measurements. 1. Introduction. The new field of compressive sensing (CS) has given us a fresh look at data acquisition, one of the fundamental tasks in signal processing. The message of this theory can be summarized succinctly [7, 8, 10, 15, 32]: the number of measurements we need to reconstruct a signal depends on its sparsity rather than its bandwidth. These measurements, however, are different than the samples that
