TY - GEN
T1 - Nonlinear compressed sensing with application to phase retrieval
AU - Beck, Amir
AU - Eldar, Yonina C.
AU - Shechtman, Y.
PY - 2013
Y1 - 2013
N2 - We extend the ideas of compressed sensing to nonlinear measurement systems. In particular, we treat the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We derive several different optimality criteria which are based on the notions of stationarity and coordinate-wise optimality. These conditions are then used to derive three numerical algorithms aimed at finding points satisfying the resulting optimality criteria: the iterative hard thresholding method and the greedy and partial sparse-simplex methods. The theoretical convergence of these methods and their relations to the derived optimality conditions are studied. We then specialize our algorithms to the problem of phase retrieval and develop an efficient method for retrieving a signal from its magnitude only measurements.
AB - We extend the ideas of compressed sensing to nonlinear measurement systems. In particular, we treat the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We derive several different optimality criteria which are based on the notions of stationarity and coordinate-wise optimality. These conditions are then used to derive three numerical algorithms aimed at finding points satisfying the resulting optimality criteria: the iterative hard thresholding method and the greedy and partial sparse-simplex methods. The theoretical convergence of these methods and their relations to the derived optimality conditions are studied. We then specialize our algorithms to the problem of phase retrieval and develop an efficient method for retrieving a signal from its magnitude only measurements.
UR - http://www.scopus.com/inward/record.url?scp=84897713165&partnerID=8YFLogxK
U2 - 10.1109/GlobalSIP.2013.6736955
DO - 10.1109/GlobalSIP.2013.6736955
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AN - SCOPUS:84897713165
SN - 9781479902484
T3 - 2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings
SP - 617
BT - 2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings
T2 - 2013 1st IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013
Y2 - 3 December 2013 through 5 December 2013
ER -