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We develop a projected Nesterov’s proximalgradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov’s momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable datafidelity (negative loglikelihood (NLL)) term and a convex regularization term. We apply sparse signal regularization where the signal belongs to a closed convex set within the closure of the domain of the NLL; the convexset constraint facilitates flexible NLL domains and accurate signal recovery. Signal sparsity is imposed using the ℓ₁norm penalty on the signal’s linear transform coefficients. The PNPG approach employs a projectedmore »

Consider reconstructing a signal x by minimizing a weighted sum of a convex differentiable negative loglikelihood (NLL) (datafidelity) term and a convex regularization term that imposes a convexset constraint on x and enforces its sparsity using ℓ1norm analysis regularization.We compute upper bounds on the regularization tuning constant beyond which the regularization term overwhelmingly dominates the NLL term so that the set of minimum points of the objective function does not change. Necessary and sufficient conditions for irrelevance of sparse signal regularization and a condition for the existence of finite upper bounds are established. We formulate an optimization problem for findingmore »

We develop a sparse image reconstruction method for Poissondistributed polychromatic Xray computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. We employ our massattenuation spectrum parameterization of the noiseless measurements for singlematerial objects and express the massattenuation spectrum as a linear combination of Bspline basis functions of order one. A block coordinatedescent algorithm is developed for constrained minimization of a penalized Poisson negative loglikelihood (NLL) cost function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and nonnegativity and sparsity of the densitymap image; themore »

We develop a framework for reconstructing images that are sparse in an appropriate transform domain from polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and incidentenergy spectrum are unknown. Assuming that the object that we wish to reconstruct consists of a single material, we obtain a parsimonious measurementmodel parameterization by changing the integral variable from photon energy to mass attenuation, which allows us to combine the variations brought by the unknown incident spectrum and mass attenuation into a single unknown massattenuation spectrum function; the resulting measurement equation has the Laplaceintegral form. Themore »

We develop a projected Nesterov’s proximalgradient (PNPG) scheme for reconstructing sparse signals from compressive Poissondistributed 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 loglikelihood (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 totalvariation (TV) penalty. We present analytical upper bounds on the regularization tuning constant. The proposed PNPG method employs projected Nesterov’s acceleration step, function restart, andmore »

We develop a sparse image reconstruction method for polychromatic tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. To obtain a parsimonious measurement model parameterization, we first rewrite the measurement equation using our mass attenuation parameterization, which has the Laplace integral form. The unknown massattenuation spectrum is expanded into basis functions using a Bspline basis of order one. We develop a block coordinatedescent algorithm for constrained minimization of a penalized negative loglikelihood function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and sparsity of themore »

In largescale wireless sensor networks, sensorprocessor elements (nodes) are densely deployed to monitor the environment; consequently, their observations form a random field that is highly correlated in space.We consider a fusion sensornetwork architecture where, due to the bandwidth and energy constraints, the nodes transmit quantized data to a fusion center. The fusion center provides feedback by broadcasting summary information to the nodes. In addition to saving energy, this feedback ensures reliability and robustness to node and fusioncenter failures. We assume that the sensor observations follow a linearregression model with known spatial covariances between any two locations within a region ofmore »