Dequantizing compressed sensing with non-gaussian constraints

Proceedings - International Conference on Image Processing, ICIP

Volumn , Issue , 2009, Pages 1465-1468

  Jacques, L ^a,b,d   Hammond, D K ^a   Fadili, M J ^c  

^a EPFL   (Switzerland)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^c UNIVERSITÉ DE CAEN   (France)

^d NATIONAL SCIENCE FOUNDATION   (United States)

Author keywords

Basis pursuit; Compressed sensing; Convex optimization; Quantization; Sampling; Uniform noise

Indexed keywords

DECODING; IMAGE RECONSTRUCTION; IMAGING SYSTEMS; MATRIX ALGEBRA; OPTIMIZATION;

BASIS PURSUITS; COMPRESSED SENSING; DATA FIDELITY; DE-NOISE; GAUSSIAN RANDOM MATRICES; HIGH PROBABILITY; MATRIX; MINIMAL VALUE; NON-GAUSSIAN; NUMERICAL EXPERIMENTS; OVERSAMPLED; QUANTIZATION DISTORTION; QUANTIZED MEASUREMENTS; RECONSTRUCTION ERROR;

CONVEX OPTIMIZATION;

EID: 77951957723     PISSN: 15224880     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICIP.2009.5414551     Document Type: Conference Paper

References (15)

1. E.J. Candès and J. Romberg, "Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions," Found. Comp. Math., 6(2):227-254, 2006.
2. H. Rauhut, K. Schnass, and P. Vandergheynst, "Compressed sensing and redundant dictionaries," IEEE T. Inform. Theory., 54(5):2210-2219, 2007.
3. E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Comm. Pure Appl. Math, 59(8):1207-1223, 2006. (Pubitemid 43988295)
4. A. Cohen, R. DeVore, and W. Dahmen, "Compressed sensing and best k-term approximation," J. Amer. Math. Soc., 22:211-231, 2009.
5. E. Candès, "The restricted isometry property and its implications for compressed sensing," Compte Rendus de l'Academie des Sciences, Paris, Serie I, 346:589-592, 2008.
6. P. Boufounos and R.G. Baraniuk, "1-bit compressive sensing," in 42nd Conf. Inf. Sc. Systems (CISS), Princeton, NJ, March 2008, 19-21.
7. W. Dai, H. Vinh Pham, and O. Milenkovic, "Distortion-rate functions for quantized compressive sensing," preprint, 2009, arXiv:0901.0749.
8. A. Zymnis, S. Boyd and E. Cand̀es, "Compressed sensing with quantized measurements," Submitted work, 2009.
9. N.T. Thao and M. Vetterli, "Deterministic analysis of oversampled A/D conversion and decoding improvement based on consistent estimates," IEEE. T. Sig. Proc., 42(3):519-531, 1994.
10. P. Weiss, L. Blanc-Feraud, T. Andre, and M. Antonini "Compression artifacts reduction using variational methods: Algorithms and experimental study Acoustics," IEEE ICASSP 2008, 1173-1176.
11. L. Jacques, D.K. Hammond, and M.J. Fadili, "Dequantizing compressed sensing: when oversampling and non-Gaussian constraints combine" http://arxiv.org/abs/0902.2367, 2009,
12. D. François, V.Wertz, and M. Verleysen, "The Concentration of Fractional Distances," IEEE T. Know. Data. Eng., 873-886, 2007.
13. W.L. Bynum, "Weak parallelogram laws for Banach spaces," Canad. Math. Bull., 19(3):269-275, 1976.
14. P.L. Combettes, "Solving monotone inclusions via compositions of nonexpansive averaged operators," Optimization, 53:475-504, 2004.
15. M. Lustig, D. Donoho and J. M. Pauly, "Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging," Magnetic Resonance in Medicine, 58:1182-1195, 2007.