Restricted Isometry Property in coded aperture compressive spectral imaging

Coded Aperture Snapshot Spectral Imaging Systems (CASSI) capture the spectral information of a scene using a set of coded focal plane array measurements. Compressed sensing reconstruction algorithms are used to reconstruct the underlying spectral 3D data cube. The coded measurements in CASSI use structured sensing matrices. This article describes the Restricted Isometry Property (RIP) for the projection matrices used in CASSI. In turn, the RIP provides guidelines for the minimum number of FPA measurement shots needed for image reconstruction. It also provides the optimal transmittance parameters for the set of code apertures used in the acquisition process.

[1]  Henry Arguello,et al.  Spectrally Selective Compressive Imaging by Matrix System Analysis , 2012 .

[2]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[3]  Xiaobai Sun,et al.  Video rate spectral imaging using a coded aperture snapshot spectral imager. , 2009, Optics express.

[4]  Ashwin A. Wagadarikar.  Compressive Spectral and Coherence Imaging , 2011 .

[5]  Henry Arguello,et al.  Code aperture optimization for spectrally agile compressive imaging. , 2011, Journal of the Optical Society of America. A, Optics, image science, and vision.

[6]  Trac D. Tran,et al.  Fast and Efficient Compressive Sensing Using Structurally Random Matrices , 2011, IEEE Transactions on Signal Processing.

[7]  M. Ledoux.  The concentration of measure phenomenon , 2001 .

[8]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.

[9]  Massimo Fornasier,et al.  Theoretical Foundations and Numerical Methods for Sparse Recovery , 2010, Radon Series on Computational and Applied Mathematics.