2015

Blind Recovery of Sparse Signals from Subsampled Convolution

Lee, Kiryung, Li, Yanjun, Junge, Marius et al.

Understand

Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution.

To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in practical applications.
In particular, sparsity models have provided promising priors.
However, in spite of empirical success of these methods in many applications, existing analyses are rather limited in two main ways: by disparity between the theoretical assumptions on the signal and/or measurement model versus practical setups; or by failure to provide a performance guarantee for parameter values within the optimal regime defined by the information theoretic limits.

Built on

P.-Å. Wedin, “Perturbation bounds in connection with singular value decomposition,” BIT Numer. Math. , vol. 12, no. 1, pp. 99–111, 1972
1972
Earlier work this paper cites.
D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. , vol. 13, no. 3, pp. 43–64, May 1996
1996
Earlier work this paper cites.
K. Abed-Meraim, W. Qiu, and Y. Hua, “Blind system identification,” Proc. IEEE , vol. 85, no. 8, pp. 1310–1322, 1997
1997
Earlier work this paper cites.
Y. Lin and D. Lee, “Relevant deconvolution for acoustic source estimation,” in Proc. ICASSP , Mar. 2005, pp. v/529–v/532
2005
Earlier work this paper cites.
E. J. Candès and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory , vol. 51, no. 12, pp. 4203–4215, 2005
2005
Earlier work this paper cites.
F. Šroubek, G. Cristóbal, and J. Flusser, “A unified approach to superresolution and multichannel blind deconvolution,” IEEE Trans. Image Process. , vol. 16, no. 9, pp. 2322–2332, 2007
2007
Earlier work this paper cites.
L. Ying and J. Sheng, “Joint image reconstruction and sensitivity estimation in SENSE (JSENSE),” Magnet. Reson. Med. , vol. 57, no. 6, pp. 1196–1202, 2007
2007
Earlier work this paper cites.
E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” Comptes Rendus Mathematique , vol. 346, no. 9, pp. 589–592, 2008
2008
Earlier work this paper cites.

Similar

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constr. Approx. , vol. 28, no. 3, pp. 253–263, 2008
2008
Cited alongside, same era.
D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. , vol. 26, no. 3, pp. 301–321, 2009
2009
Cited alongside, same era.
W. Dai and O. Milenkovic, “Subspace pursuit for compressive sensing signal reconstruction,” IEEE Trans. Inf. Theory , vol. 55, no. 5, pp. 2230–2249, May 2009
2009
Cited alongside, same era.
E. J. Candès and T. Tao, “The power of convex relaxation: Near-optimal matrix completion,” IEEE Trans. Inf. Theory , vol. 56, no. 5, pp. 2053–2080, 2010
2010
Cited alongside, same era.
S. Foucart, “Hard thresholding pursuit: an algorithm for compressive sensing,” SIAM J. Numer. Anal. , vol. 49, no. 6, pp. 2543–2563, 2011
2011
Cited alongside, same era.
J. Kotera, F. Šroubek, and P. Milanfar, “Blind deconvolution using alternating maximum a posteriori estimation with heavy-tailed priors,” in Comput. Anal. Images Patterns . Springer, 2013, pp. 59–66
2013
Cited alongside, same era.
K. Lee, Y. Wu, and Y. Bresler, “Near optimal compressed sensing of sparse rank-one matrices via sparse power factorization,” arXiv preprint arXiv:1312.0525 , 2013
Original
2013
Cited alongside, same era.
N. Kazemi and M. D. Sacchi, “Sparse multichannel blind deconvolution,” Geophysics , vol. 79, no. 5, pp. V143–V152, 2014
2014
Cited alongside, same era.
K. Lee and M. Junge, “RIP-like properties in subsampled blind deconvolution,” arXiv preprint arXiv:1511.06146
Original
Cited in the paper.

Then

A. Ahmed, B. Recht, and J. Romberg, “Blind deconvolution using convex programming,” IEEE Trans. Inf. Theory , vol. 60, no. 3, pp. 1711–1732, Mar. 2014
2014
Later among the works it cites.
S. Choudhary and U. Mitra, “Identifiability scaling laws in bilinear inverse problems,” arXiv preprint arXiv:1402.2637 , 2014
Original
2014
Later among the works it cites.
S. Choudhary and U. Mitra, “Sparse blind deconvolution: What cannot be done,” in Proc. ISIT , Jun. 2014, pp. 3002–3006
2014
Later among the works it cites.
S. Ling and T. Strohmer, “Self-calibration and biconvex compressive sensing,” arXiv preprint arXiv:1501.06864 , 2015
Original
2015
Closest in time.
Y. Chi, “Guaranteed blind sparse spikes deconvolution via lifting and convex optimization,” arXiv preprint arXiv:1506.02751 , 2015
Original
2015
Closest in time.
Y. Li, K. Lee, and Y. Bresler, “A unified framework for identifiability analysis in bilinear inverse problems with applications to subspace and sparsity models,” arXiv preprint arXiv:1501.06120 , 2015
Original
2015
Closest in time.
——, “Identifiability in blind deconvolution with subspace or sparsity constraints,” arXiv preprint arXiv:1505.03399 , 2015
Original
2015
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…