Imaging via Compressive Sampling

Image compression algorithms convert high-resolution images into a relatively small bit streams in effect turning a large digital data set into a substantially smaller one. This article introduces compressive sampling and recovery using convex programming.

[1]  PROCEssIng magazInE.  IEEE Signal Processing Magazine , 2004 .

[2]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[3]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[4]  Touradj Ebrahimi,et al.  The JPEG 2000 still image compression standard , 2001, IEEE Signal Process. Mag..

[5]  M. Rudelson,et al.  Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements , 2006, 2006 40th Annual Conference on Information Sciences and Systems.

[6]  Xiaoming Huo,et al.  Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.

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

[8]  Martin Vetterli,et al.  Data Compression and Harmonic Analysis , 1998, IEEE Trans. Inf. Theory.

[9]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

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

[11]  E. Candès,et al.  Sparsity and incoherence in compressive sampling , 2006, math/0611957.

[12]  Terence Tao,et al.  The Dantzig selector: Statistical estimation when P is much larger than n , 2005, math/0506081.

[13]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[14]  Joan L. Mitchell,et al.  JPEG: Still Image Data Compression Standard , 1992 .

[15]  Abhishek Bandyopadhyay,et al.  Image processing system using a programmable transform imager , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

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

[17]  P. Laguna,et al.  Signal Processing , 2002, Yearbook of Medical Informatics.

[18]  M. Rudelson,et al.  On sparse reconstruction from Fourier and Gaussian measurements , 2008 .

[19]  Emmanuel J. Cand.  REJOINDER: THE DANTZIG SELECTOR: STATISTICAL ESTIMATION WHEN P IS MUCH LARGER THAN N , 2007 .

[20]  Balas K. Natarajan,et al.  Sparse Approximate Solutions to Linear Systems , 1995, SIAM J. Comput..

[21]  D. Donoho,et al.  Neighborliness of randomly projected simplices in high dimensions. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Jerome M. Shapiro,et al.  Embedded image coding using zerotrees of wavelet coefficients , 1993, IEEE Trans. Signal Process..

[23]  Joel A. Tropp,et al.  Just relax: convex programming methods for identifying sparse signals in noise , 2006, IEEE Transactions on Information Theory.

[24]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[25]  R. DeVore,et al.  Nonlinear approximation , 1998, Acta Numerica.

[26]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[27]  David V. Anderson,et al.  Compressive Sensing on a CMOS Separable-Transform Image Sensor , 2010, Proceedings of the IEEE.