1,351 research outputs found

    Variational Bayesian algorithm for quantized compressed sensing

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    Compressed sensing (CS) is on recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior and digital quantization of the measurement data is inevitable in practical implementation of CS algorithms. In the existing literature, the quantization error is modeled typically as additive noise and the multi-bit and 1-bit quantized CS problems are dealt with separately using different treatments and procedures. In this paper, a novel variational Bayesian inference based CS algorithm is presented, which unifies the multi- and 1-bit CS processing and is applicable to various cases of noiseless/noisy environment and unsaturated/saturated quantizer. By decoupling the quantization error from the measurement noise, the quantization error is modeled as a random variable and estimated jointly with the signal being recovered. Such a novel characterization of the quantization error results in superior performance of the algorithm which is demonstrated by extensive simulations in comparison with state-of-the-art methods for both multi-bit and 1-bit CS problems.Comment: Accepted by IEEE Trans. Signal Processing. 10 pages, 6 figure

    Optimal Quantization for Compressive Sensing under Message Passing Reconstruction

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    We consider the optimal quantization of compressive sensing measurements following the work on generalization of relaxed belief propagation (BP) for arbitrary measurement channels. Relaxed BP is an iterative reconstruction scheme inspired by message passing algorithms on bipartite graphs. Its asymptotic error performance can be accurately predicted and tracked through the state evolution formalism. We utilize these results to design mean-square optimal scalar quantizers for relaxed BP signal reconstruction and empirically demonstrate the superior error performance of the resulting quantizers.Comment: 5 pages, 3 figures, submitted to IEEE International Symposium on Information Theory (ISIT) 2011; minor corrections in v

    Signal Recovery From 1-Bit Quantized Noisy Samples via Adaptive Thresholding

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    In this paper, we consider the problem of signal recovery from 1-bit noisy measurements. We present an efficient method to obtain an estimation of the signal of interest when the measurements are corrupted by white or colored noise. To the best of our knowledge, the proposed framework is the pioneer effort in the area of 1-bit sampling and signal recovery in providing a unified framework to deal with the presence of noise with an arbitrary covariance matrix including that of the colored noise. The proposed method is based on a constrained quadratic program (CQP) formulation utilizing an adaptive quantization thresholding approach, that further enables us to accurately recover the signal of interest from its 1-bit noisy measurements. In addition, due to the adaptive nature of the proposed method, it can recover both fixed and time-varying parameters from their quantized 1-bit samples.Comment: This is a pre-print version of the original conference paper that has been accepted at the 2018 IEEE Asilomar Conference on Signals, Systems, and Computer
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