Quantization error and dynamic range considerations for compressive imaging systems design.

A natural field of application for compressive sensing theory is imaging. Indeed, numerous compressive imaging (CI) systems and applications have been developed during the last few years. This work addresses the quantization effect in CI, which is fundamental for most CI architectures. In this paper, the implications of sensor quantization on universal CI are investigated theoretically and demonstrated with numerical experiments. It is shown that employing a CI framework may set severe requirements on the quantization depth of the optical sensor used. The quantization depth overhead requirement may be prohibitive in many optical imaging scenarios employing typical CI architectures. Practical solutions that significantly alleviate this requirement are suggested.

[1]  Jun Tanida,et al.  Generalized sampling using a compound-eye imaging system for multi-dimensional object acquisition. , 2010, Optics express.

[2]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[3]  Wai Lam Chan,et al.  A single-pixel terahertz imaging system based on compressed sensing , 2008 .

[4]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[5]  Rebecca Willett,et al.  Compressive coded aperture imaging , 2009, Electronic Imaging.

[6]  Myungjin Cho,et al.  3D passive integral imaging using compressive sensing. , 2012, Optics express.

[7]  Joseph N Mait,et al.  Millimeter-wave compressive holography. , 2010, Applied optics.

[8]  A. Stern,et al.  Random Projections Imaging With Extended Space-Bandwidth Product , 2007, Journal of Display Technology.

[9]  Edmund Y Lam,et al.  Object reconstruction in block-based compressive imaging. , 2012, Optics express.

[10]  Richard G. Baraniuk,et al.  A new compressive imaging camera architecture using optical-domain compression , 2006, Electronic Imaging.

[11]  Yonina C. Eldar,et al.  Super-resolution and reconstruction of sparse images carried by incoherent light. , 2010, Optics letters.

[12]  Ofer Levi,et al.  Optical compressive change and motion detection. , 2012, Applied optics.

[13]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[14]  Ao Tang,et al.  A Unique “Nonnegative” Solution to an Underdetermined System: From Vectors to Matrices , 2010, IEEE Transactions on Signal Processing.

[15]  Adrian Stern,et al.  Compressed imaging system with linear sensors. , 2007, Optics letters.

[16]  Richard G. Baraniuk,et al.  Terahertz imaging with compressed sensing and phase retrieval , 2008 .

[17]  Yonina C Eldar,et al.  Super-resolution and reconstruction of sparse sub-wavelength images. , 2009, Optics express.

[18]  R. M. Willett,et al.  Compressed sensing for practical optical imaging systems: A tutorial , 2011, IEEE Photonics Conference 2012.

[19]  José M. Bioucas-Dias,et al.  A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration , 2007, IEEE Transactions on Image Processing.

[20]  Michael Unser,et al.  Optical imaging using binary sensors. , 2010, Optics express.

[21]  Bahram Javidi,et al.  Multidimensional imaging using compressive Fresnel holography. , 2012, Optics letters.

[22]  Bahram Javidi,et al.  Single exposure super-resolution compressive imaging by double phase encoding. , 2010, Optics express.

[23]  Faramarz Farahi,et al.  Active illumination single-pixel camera based on compressive sensing. , 2011, Applied optics.

[24]  M E Gehm,et al.  Static compressive tracking. , 2012, Optics express.

[25]  Adrian Stern,et al.  Recovery of partially occluded objects by applying compressive Fresnel holography. , 2012, Optics letters.

[26]  Michael Elad,et al.  On the Uniqueness of Nonnegative Sparse Solutions to Underdetermined Systems of Equations , 2008, IEEE Transactions on Information Theory.

[27]  Jun Ke,et al.  Optical architectures for compressive imaging , 2007 .