Rate-distortion performance of compressive sensing in single pixel camera

Compressive Sensing is an alternative to the acquisition and compression of sparse signals. One of the CS applications is the single pixel camera that reconsiders the conventional imaging systems. The key part of the camera is a Digital Micro-mirror Device (DMD), which is operated by a binary sensing matrix. The paper objective is to evaluate the CS performances in the case of three different binary sensing matrices - Binary Random (BRandom), Binary Sparse (BSparse) and Low Density Parity Check (LDPC) code - and three sparsifying transforms: Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT) and Total Variation (TV). The study concerns numeric images and it is done from the perspective of the Rate-Distortion characteristic. The experimental results indicate the couple LDPC - TV as the best solution and proves that visually lossless compression can be obtained by this approach.

[1]  Piotr Indyk,et al.  Sparse Recovery Using Sparse Random Matrices , 2010, LATIN.

[2]  Abdorreza Heidari,et al.  A 2D camera design with a single-pixel detector , 2009, 2009 34th International Conference on Infrared, Millimeter, and Terahertz Waves.

[3]  Shuhong Jiao,et al.  Compressed sensing and reconstruction with Semi-Hadamard matrices , 2010, 2010 2nd International Conference on Signal Processing Systems.

[4]  Ting Sun,et al.  Single-pixel imaging via compressive sampling , 2008, IEEE Signal Process. Mag..

[5]  Joachim H. G. Ender,et al.  On compressive sensing applied to radar , 2010, Signal Process..

[6]  Kidiyo Kpalma,et al.  Sparse Binary Matrices of LDPC Codes for Compressed Sensing , 2012, 2012 Data Compression Conference.

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

[8]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[9]  Kidiyo Kpalma,et al.  Near-optimal Binary Compressed Sensing Matrix , 2013, ArXiv.

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

[11]  Luiz Velho,et al.  On the empirical rate-distortion performance of Compressive Sensing , 2009, 2009 16th IEEE International Conference on Image Processing (ICIP).

[12]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

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

[14]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[15]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[16]  Leslie N. Smith.  How to find real-world applications of compressive sensing , 2013, Defense, Security, and Sensing.