56 research outputs found
Empirical Bayes and Full Bayes for Signal Estimation
We consider signals that follow a parametric distribution where the parameter
values are unknown. To estimate such signals from noisy measurements in scalar
channels, we study the empirical performance of an empirical Bayes (EB)
approach and a full Bayes (FB) approach. We then apply EB and FB to solve
compressed sensing (CS) signal estimation problems by successively denoising a
scalar Gaussian channel within an approximate message passing (AMP) framework.
Our numerical results show that FB achieves better performance than EB in
scalar channel denoising problems when the signal dimension is small. In the CS
setting, the signal dimension must be large enough for AMP to work well; for
large signal dimensions, AMP has similar performance with FB and EB.Comment: This work was presented at the Information Theory and Application
workshop (ITA), San Diego, CA, Feb. 201
Approximate Message Passing in Coded Aperture Snapshot Spectral Imaging
We consider a compressive hyperspectral imaging reconstruction problem, where
three-dimensional spatio-spectral information about a scene is sensed by a
coded aperture snapshot spectral imager (CASSI). The approximate message
passing (AMP) framework is utilized to reconstruct hyperspectral images from
CASSI measurements, and an adaptive Wiener filter is employed as a
three-dimensional image denoiser within AMP. We call our algorithm
"AMP-3D-Wiener." The simulation results show that AMP-3D-Wiener outperforms
existing widely-used algorithms such as gradient projection for sparse
reconstruction (GPSR) and two-step iterative shrinkage/thresholding (TwIST)
given the same amount of runtime. Moreover, in contrast to GPSR and TwIST,
AMP-3D-Wiener need not tune any parameters, which simplifies the reconstruction
process.Comment: to appear in Globalsip 201
Precise Phase Transition of Total Variation Minimization
Characterizing the phase transitions of convex optimizations in recovering
structured signals or data is of central importance in compressed sensing,
machine learning and statistics. The phase transitions of many convex
optimization signal recovery methods such as minimization and nuclear
norm minimization are well understood through recent years' research. However,
rigorously characterizing the phase transition of total variation (TV)
minimization in recovering sparse-gradient signal is still open. In this paper,
we fully characterize the phase transition curve of the TV minimization. Our
proof builds on Donoho, Johnstone and Montanari's conjectured phase transition
curve for the TV approximate message passing algorithm (AMP), together with the
linkage between the minmax Mean Square Error of a denoising problem and the
high-dimensional convex geometry for TV minimization.Comment: 6 page
Maximin Analysis of Message Passing Algorithms for Recovering Block Sparse Signals
We consider the problem of recovering a block (or group) sparse signal from
an underdetermined set of random linear measurements, which appear in
compressed sensing applications such as radar and imaging. Recent results of
Donoho, Johnstone, and Montanari have shown that approximate message passing
(AMP) in combination with Stein's shrinkage outperforms group LASSO for large
block sizes. In this paper, we prove that, for a fixed block size and in the
strong undersampling regime (i.e., having very few measurements compared to the
ambient dimension), AMP cannot improve upon group LASSO, thereby complementing
the results of Donoho et al
Ultra Low-Complexity Detection of Spectrum Holes in Compressed Wideband Spectrum Sensing
Wideband spectrum sensing is a significant challenge in cognitive radios
(CRs) due to requiring very high-speed analog- to-digital converters (ADCs),
operating at or above the Nyquist rate. Here, we propose a very low-complexity
zero-block detection scheme that can detect a large fraction of spectrum holes
from the sub-Nyquist samples, even when the undersampling ratio is very small.
The scheme is based on a block sparse sensing matrix, which is implemented
through the design of a novel analog-to- information converter (AIC). The
proposed scheme identifies some measurements as being zero and then verifies
the sub-channels associated with them as being vacant. Analytical and
simulation results are presented that demonstrate the effectiveness of the
proposed method in reliable detection of spectrum holes with complexity much
lower than existing schemes. This work also introduces a new paradigm in
compressed sensing where one is interested in reliable detection of (some of
the) zero blocks rather than the recovery of the whole block sparse signal.Comment: 7 pages, 5 figure
- …