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This paper studies the problem of power allocation in compressed sensing when different components in the unknown sparse signal have different probability to be non-zero. Given the prior information of the non-uniform sparsity and the total power budget, we are interested in how to optimally allocate the power across the columns of a Gaussian random measurement matrix so that the mean squared reconstruction error is minimized. Based on the state evolution technique originated from the work by Donoho, Maleki, and Montanari, we revise the so called approximate message passing (AMP) algorithm for the reconstruction and quantify the MSE performance in the asymptotic regime. Then the closed form of the optimal power allocation is obtained. The results show that in the presence of measurement noise, uniform power allocation, which results in the commonly used Gaussian random matrix with i.i.d. entries, is not optimal for non-uniformly sparse signals. Empirical results are presented to demonstrate the performance gain.
Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear minimization proce
Advances of information-theoretic understanding of sparse sampling of continuous uncoded signals at sampling rates exceeding the Landau rate were reported in recent works. This work examines sparse sampling of coded signals at sub-Landau sampling rat
Xampling generalizes compressed sensing (CS) to reduced-rate sampling of analog signals. A unified framework is introduced for low rate sampling and processing of signals lying in a union of subspaces. Xampling consists of two main blocks: Analog com
Goal: This paper deals with the problems that some EEG signals have no good sparse representation and single channel processing is not computationally efficient in compressed sensing of multi-channel EEG signals. Methods: An optimization model with L
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The current acquis