TY - GEN
T1 - Stability in blind deconvolution of sparse signals and reconstruction by alternating minimization
AU - Lee, Kiryung
AU - Li, Yanjun
AU - Junge, Marius
AU - Bresler, Yoram
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/7/2
Y1 - 2015/7/2
N2 - Blind deconvolution is the recovery of two unknown signals from 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. In spite of empirical success in many applications, existing analyses are rather limited in two main ways: by disparity between theoretical assumptions on the signal and/or measurement model versus practical setups; or by failure to demonstrate success for parameter values within the optimal regime defined by the information theoretic limits. In particular, it has been shown that a naive sparsity model is not strong enough as a prior for identifiability in blind deconvolution problem. In addition to sparsity, we adopt a conic constraint by Ahmed et al., which enforces flat spectra in the Fourier domain. Under this prior, we provide an iterative algorithm that achieves guaranteed performance in blind deconvolution with number of measurements proportional (up to a logarithmic factor) to the sparsity level of the signal.
AB - Blind deconvolution is the recovery of two unknown signals from 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. In spite of empirical success in many applications, existing analyses are rather limited in two main ways: by disparity between theoretical assumptions on the signal and/or measurement model versus practical setups; or by failure to demonstrate success for parameter values within the optimal regime defined by the information theoretic limits. In particular, it has been shown that a naive sparsity model is not strong enough as a prior for identifiability in blind deconvolution problem. In addition to sparsity, we adopt a conic constraint by Ahmed et al., which enforces flat spectra in the Fourier domain. Under this prior, we provide an iterative algorithm that achieves guaranteed performance in blind deconvolution with number of measurements proportional (up to a logarithmic factor) to the sparsity level of the signal.
UR - http://www.scopus.com/inward/record.url?scp=84941063996&partnerID=8YFLogxK
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U2 - 10.1109/SAMPTA.2015.7148871
DO - 10.1109/SAMPTA.2015.7148871
M3 - Conference contribution
AN - SCOPUS:84941063996
T3 - 2015 International Conference on Sampling Theory and Applications, SampTA 2015
SP - 158
EP - 162
BT - 2015 International Conference on Sampling Theory and Applications, SampTA 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 11th International Conference on Sampling Theory and Applications, SampTA 2015
Y2 - 25 May 2015 through 29 May 2015
ER -