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Projected Nesterov’S Proximal-Gradient Signal Recovery From Compressive Poisson Measurements, Renliang Gu, Aleksandar Dogandžić

Aleksandar Dogandžić

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 …