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Title: Projected Nesterov's proximal-gradient signal recovery from compressive poisson measurements
We develop a projected Nesterov’s proximal-gradient (PNPG) scheme for reconstructing sparse signals from compressive Poisson-distributed measurements with the mean signal intensity that follows an affine model with known intercept. The objective function to be minimized is a sum of convex data fidelity (negative log-likelihood (NLL)) and regularization terms. We apply sparse signal regularization where the signal belongs to a nonempty closed convex set within the domain of the NLL and signal sparsity is imposed using total-variation (TV) penalty. We present analytical upper bounds on the regularization tuning constant. The proposed PNPG method employs projected Nesterov’s acceleration step, function restart, and an adaptive step-size selection scheme that aims at obtaining a good local majorizing function of the NLL and reducing the time spent backtracking. We establish O(k⁻²) convergence of the PNPG method with step-size backtracking only and no restart. Numerical examples demonstrate the performance of the PNPG method.
Authors:
;
Award ID(s):
1421480
Publication Date:
NSF-PAR ID:
10016192
Journal Name:
Proc. 49th Asilomar Conference on Signals, Systems and Computers
Page Range or eLocation-ID:
1490 to 1495
Sponsoring Org:
National Science Foundation
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