Band-limited random waveforms in compressive radar imaging

Mahesh C. Shastry, Ram M. Narayanan, Muralidhar Rangaswamy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Compressive sensing makes it possible to recover sparse target scenes from under-sampled measurements when uncorrelated random-noise waveforms are used as probing signals. The mathematical theory behind this assertion is based on the fact that Toeplitz and circulant random matrices generated from independent identically distributed (i.i.d) Gaussian random sequences satisfy the restricted isometry property. In real systems, waveforms have smooth, non-ideal autocorrelation functions, thereby degrading the performance of compressive sensing algorithms. In this paper, we extend the existing theory to incorporate such non-idealities into the analysis of compressive recovery. The presence of extended scatterers also causes distortions due to the correlation between different cells of the target scene. Extended targets make the target scene more dense, causing random transmit waveforms to be sub-optimal for recovery. We propose to incorporate extended targets by considering them to be sparsely representable in redundant dictionaries. We demonstrate that a low complexity algorithm to optimize the transmit waveform leads to improved performance.

Original languageEnglish (US)
Title of host publicationCompressive Sensing
DOIs
StatePublished - Jul 23 2012
EventCompressive Sensing - Baltimore, MD, United States
Duration: Apr 26 2012Apr 27 2012

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume8365
ISSN (Print)0277-786X

Other

OtherCompressive Sensing
CountryUnited States
CityBaltimore, MD
Period4/26/124/27/12

Fingerprint

imaging radar
Radar Imaging
Radar imaging
Waveform
waveforms
Recovery
Target
Glossaries
Compressive Sensing
Autocorrelation
recovery
dictionaries
Circulant Matrix
Random Noise
Random Sequence
Otto Toeplitz
Autocorrelation Function
random noise
Random Matrices
Assertion

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Shastry, M. C., Narayanan, R. M., & Rangaswamy, M. (2012). Band-limited random waveforms in compressive radar imaging. In Compressive Sensing [83650U] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 8365). https://doi.org/10.1117/12.920936
Shastry, Mahesh C. ; Narayanan, Ram M. ; Rangaswamy, Muralidhar. / Band-limited random waveforms in compressive radar imaging. Compressive Sensing. 2012. (Proceedings of SPIE - The International Society for Optical Engineering).
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Shastry, MC, Narayanan, RM & Rangaswamy, M 2012, Band-limited random waveforms in compressive radar imaging. in Compressive Sensing., 83650U, Proceedings of SPIE - The International Society for Optical Engineering, vol. 8365, Compressive Sensing, Baltimore, MD, United States, 4/26/12. https://doi.org/10.1117/12.920936

Band-limited random waveforms in compressive radar imaging. / Shastry, Mahesh C.; Narayanan, Ram M.; Rangaswamy, Muralidhar.

Compressive Sensing. 2012. 83650U (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 8365).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Shastry MC, Narayanan RM, Rangaswamy M. Band-limited random waveforms in compressive radar imaging. In Compressive Sensing. 2012. 83650U. (Proceedings of SPIE - The International Society for Optical Engineering). https://doi.org/10.1117/12.920936