11,301 research outputs found

    Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

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    We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By relying on tools from the theory of splines, we derive the joint a priori distribution of the samples and show how this probability density function can be factorized. The factorization enables us to tractably implement the maximum a posteriori and minimum mean-square error (MMSE) criteria as two statistical approaches for estimating the unknowns. We compare the derived statistical methods with well-known techniques for the recovery of sparse signals, such as the â„“1\ell_1 norm and Log (â„“1\ell_1-â„“0\ell_0 relaxation) regularization methods. The simulation results show that, under certain conditions, the performance of the regularization techniques can be very close to that of the MMSE estimator.Comment: To appear in IEEE TS

    A Fast Blind Impulse Detector for Bernoulli-Gaussian Noise in Underspread Channel

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    The Bernoulli-Gaussian (BG) model is practical to characterize impulsive noises that widely exist in various communication systems. To estimate the BG model parameters from noise measurements, a precise impulse detection is essential. In this paper, we propose a novel blind impulse detector, which is proven to be fast and accurate for BG noise in underspread communication channels.Comment: v2 to appear in IEEE ICC 2018, Kansas City, MO, USA, May 2018 Minor erratums added in v

    Statistical Physics Analysis of Maximum a Posteriori Estimation for Multi-channel Hidden Markov Models

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    The performance of Maximum a posteriori (MAP) estimation is studied analytically for binary symmetric multi-channel Hidden Markov processes. We reduce the estimation problem to a 1D Ising spin model and define order parameters that correspond to different characteristics of the MAP-estimated sequence. The solution to the MAP estimation problem has different operational regimes separated by first order phase transitions. The transition points for LL-channel system with identical noise levels, are uniquely determined by LL being odd or even, irrespective of the actual number of channels. We demonstrate that for lower noise intensities, the number of solutions is uniquely determined for odd LL, whereas for even LL there are exponentially many solutions. We also develop a semi analytical approach to calculate the estimation error without resorting to brute force simulations. Finally, we examine the tradeoff between a system with single low-noise channel and one with multiple noisy channels.Comment: The paper has been submitted to Journal of Statistical Physics with submission number JOSS-S-12-0039
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