491 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
Vector Approximate Message Passing for the Generalized Linear Model
The generalized linear model (GLM), where a random vector is
observed through a noisy, possibly nonlinear, function of a linear transform
output , arises in a range of applications such
as robust regression, binary classification, quantized compressed sensing,
phase retrieval, photon-limited imaging, and inference from neural spike
trains. When is large and i.i.d. Gaussian, the generalized
approximate message passing (GAMP) algorithm is an efficient means of MAP or
marginal inference, and its performance can be rigorously characterized by a
scalar state evolution. For general , though, GAMP can
misbehave. Damping and sequential-updating help to robustify GAMP, but their
effects are limited. Recently, a "vector AMP" (VAMP) algorithm was proposed for
additive white Gaussian noise channels. VAMP extends AMP's guarantees from
i.i.d. Gaussian to the larger class of rotationally invariant
. In this paper, we show how VAMP can be extended to the GLM.
Numerical experiments show that the proposed GLM-VAMP is much more robust to
ill-conditioning in than damped GAMP
Sparse Estimation with the Swept Approximated Message-Passing Algorithm
Approximate Message Passing (AMP) has been shown to be a superior method for
inference problems, such as the recovery of signals from sets of noisy,
lower-dimensionality measurements, both in terms of reconstruction accuracy and
in computational efficiency. However, AMP suffers from serious convergence
issues in contexts that do not exactly match its assumptions. We propose a new
approach to stabilizing AMP in these contexts by applying AMP updates to
individual coefficients rather than in parallel. Our results show that this
change to the AMP iteration can provide theoretically expected, but hitherto
unobtainable, performance for problems on which the standard AMP iteration
diverges. Additionally, we find that the computational costs of this swept
coefficient update scheme is not unduly burdensome, allowing it to be applied
efficiently to signals of large dimensionality.Comment: 11 pages, 3 figures, implementation available at
https://github.com/eric-tramel/SwAMP-Dem
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