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**1 - 2**of**2**### DISTRIBUTED COMPRESSED SENSING OF NON-NEGATIVE SIGNALS USING SYMMETRIC ALPHA-STABLE DISTRIBUTIONS

"... Sensor networks gather an enormous amount of data over space and time to derive an estimate of a parameter or function. Several constraints, such as limited power, bandwidth, and storage capacity, motivate the need for a new paradigm for sensor data processing in order to extend the network’s lifeti ..."

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Sensor networks gather an enormous amount of data over space and time to derive an estimate of a parameter or function. Several constraints, such as limited power, bandwidth, and storage capacity, motivate the need for a new paradigm for sensor data processing in order to extend the network’s lifetime, while also obtaining accurate estimates. In a companion paper [1], we proposed a novel iterative algorithm for reconstructing non-negative sparse signals in highly impulsive background by modeling their prior distribution using symmetric alpha-stable distributions. In the present work, we extend this algorithm in the framework of distributed compressed sensing using duality theory and the method of subgradients for the optimization of the associated cost function. The experimental results show that our proposed distributed method maintains the reconstruction performance of its centralized counterpart, while also achieving a highly sparse basis configuration, thus reducing the total amount of data handled by each sensor. 1.

### Projection Onto Convex Sets (POCS) Based Signal Reconstruction Framework with an

, 2014

"... A new signal processing framework based on the projections onto convex sets (POCS) is developed for solving convex optimization problems. The di-mension of the minimization problem is lifted by one and the convex sets corresponding to the epigraph of the cost function are defined. If the cost functi ..."

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A new signal processing framework based on the projections onto convex sets (POCS) is developed for solving convex optimization problems. The di-mension of the minimization problem is lifted by one and the convex sets corresponding to the epigraph of the cost function are defined. If the cost function is a convex function in RN the corresponding epigraph set is also a convex set in RN+1. The iterative optimization approach starts with an arbitrary initial estimate in RN+1 and orthogonal projections are performed onto epigraph set in a sequential manner at each step of the optimization problem. The method provides globally optimal solutions in total-variation (TV), filtered variation (FV), `1, `1, and entropic cost functions. New de-noising and compressive sensing algorithms using the TV cost function are developed. The new algorithms do not require any of the regularization parameter adjustment. Simulation examples are presented. 1