Image reconstruction by deterministic compressed sensing with chirp matrices

Kangyu Ni, Prasun Mahanti, Somantika Datta, Svetlana Roudenko, Douglas Cochran

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

7 Citations (Scopus)

Abstract

A recently proposed approach for compressed sensing, or compressive sampling, with deterministic measurement matrices made of chirps is applied to images that possess varying degrees of sparsity in their wavelet representations. The "fast reconstruction" algorithm enabled by this deterministic sampling scheme as developed by Applebaum et al. [1] produces accurate results, but its speed is hampered when the degree of sparsity is not sufficiently high. This paper proposes an efficient reconstruction algorithm that utilizes discrete chirp-Fourier transform (DCFT) and updated linear least squares solutions and is suitable for medical images, which have good sparsity properties. Several experiments show the proposed algorithm is effective in both reconstruction fidelity and speed.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Volume7497
DOIs
StatePublished - 2009
EventMIPPR 2009 - Medical Imaging, Parallel Processing of Images, and Optimization Techniques: 6th International Symposium on Multispectral Image Processing and Pattern Recognition - Yichang, China
Duration: Oct 30 2009Nov 1 2009

Other

OtherMIPPR 2009 - Medical Imaging, Parallel Processing of Images, and Optimization Techniques: 6th International Symposium on Multispectral Image Processing and Pattern Recognition
CountryChina
CityYichang
Period10/30/0911/1/09

Fingerprint

Compressed sensing
Compressed Sensing
Chirp
Image Reconstruction
image reconstruction
chirp
Image reconstruction
Sparsity
Reconstruction Algorithm
matrices
sampling
Sampling
Least-squares Solution
Linear Least Squares
Medical Image
Fidelity
Fast Algorithm
Fourier transform
Fourier transforms
Wavelets

Keywords

  • Chirp
  • Compressed sensing
  • Discrete chirp-Fourier transform
  • Image reconstruction

ASJC Scopus subject areas

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

Cite this

Ni, K., Mahanti, P., Datta, S., Roudenko, S., & Cochran, D. (2009). Image reconstruction by deterministic compressed sensing with chirp matrices. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 7497). [74971S] https://doi.org/10.1117/12.832649

Image reconstruction by deterministic compressed sensing with chirp matrices. / Ni, Kangyu; Mahanti, Prasun; Datta, Somantika; Roudenko, Svetlana; Cochran, Douglas.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7497 2009. 74971S.

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

Ni, K, Mahanti, P, Datta, S, Roudenko, S & Cochran, D 2009, Image reconstruction by deterministic compressed sensing with chirp matrices. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 7497, 74971S, MIPPR 2009 - Medical Imaging, Parallel Processing of Images, and Optimization Techniques: 6th International Symposium on Multispectral Image Processing and Pattern Recognition, Yichang, China, 10/30/09. https://doi.org/10.1117/12.832649
Ni K, Mahanti P, Datta S, Roudenko S, Cochran D. Image reconstruction by deterministic compressed sensing with chirp matrices. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7497. 2009. 74971S https://doi.org/10.1117/12.832649
Ni, Kangyu ; Mahanti, Prasun ; Datta, Somantika ; Roudenko, Svetlana ; Cochran, Douglas. / Image reconstruction by deterministic compressed sensing with chirp matrices. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7497 2009.
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