1,351 research outputs found
Variational Bayesian algorithm for quantized compressed sensing
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
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
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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