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Full-Text Articles in Physical Sciences and Mathematics
Projected Nesterov’S Proximal-Gradient Signal Recovery From Compressive Poisson Measurements, Renliang Gu, Aleksandar Dogandžić
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 …
Markov Chain Monte Carlo Defect Identification In Nde Images, Aleksandar Dogandžić, Benhong Zhang
Markov Chain Monte Carlo Defect Identification In Nde Images, Aleksandar Dogandžić, Benhong Zhang
Aleksandar Dogandžić
We derive a hierarchical Bayesian method for identifying elliptically‐shaped regions with elevated signal levels in NDE images. We adopt a simple elliptical parametric model for the shape of the defect region and assume that the defect signals within this region are random following a truncated Gaussian distribution. Our truncated‐Gaussian model ensures that the signals within the defect region are higher than the baseline level corresponding to the noise‐only case. We derive a closed‐form expression for the kernel of the posterior probability distribution of the location, shape, and defect‐signal distribution parameters (model parameters). This result is then used to develop Markov …