1,174 research outputs found
Scampi: a robust approximate message-passing framework for compressive imaging
Reconstruction of images from noisy linear measurements is a core problem in
image processing, for which convex optimization methods based on total
variation (TV) minimization have been the long-standing state-of-the-art. We
present an alternative probabilistic reconstruction procedure based on
approximate message-passing, Scampi, which operates in the compressive regime,
where the inverse imaging problem is underdetermined. While the proposed method
is related to the recently proposed GrAMPA algorithm of Borgerding, Schniter,
and Rangan, we further develop the probabilistic approach to compressive
imaging by introducing an expectation-maximizaiton learning of model
parameters, making the Scampi robust to model uncertainties. Additionally, our
numerical experiments indicate that Scampi can provide reconstruction
performance superior to both GrAMPA as well as convex approaches to TV
reconstruction. Finally, through exhaustive best-case experiments, we show that
in many cases the maximal performance of both Scampi and convex TV can be quite
close, even though the approaches are a prori distinct. The theoretical reasons
for this correspondence remain an open question. Nevertheless, the proposed
algorithm remains more practical, as it requires far less parameter tuning to
perform optimally.Comment: Presented at the 2015 International Meeting on High-Dimensional Data
Driven Science, Kyoto, Japa
Off-the-Grid Line Spectrum Denoising and Estimation with Multiple Measurement Vectors
Compressed Sensing suggests that the required number of samples for
reconstructing a signal can be greatly reduced if it is sparse in a known
discrete basis, yet many real-world signals are sparse in a continuous
dictionary. One example is the spectrally-sparse signal, which is composed of a
small number of spectral atoms with arbitrary frequencies on the unit interval.
In this paper we study the problem of line spectrum denoising and estimation
with an ensemble of spectrally-sparse signals composed of the same set of
continuous-valued frequencies from their partial and noisy observations. Two
approaches are developed based on atomic norm minimization and structured
covariance estimation, both of which can be solved efficiently via semidefinite
programming. The first approach aims to estimate and denoise the set of signals
from their partial and noisy observations via atomic norm minimization, and
recover the frequencies via examining the dual polynomial of the convex
program. We characterize the optimality condition of the proposed algorithm and
derive the expected convergence rate for denoising, demonstrating the benefit
of including multiple measurement vectors. The second approach aims to recover
the population covariance matrix from the partially observed sample covariance
matrix by motivating its low-rank Toeplitz structure without recovering the
signal ensemble. Performance guarantee is derived with a finite number of
measurement vectors. The frequencies can be recovered via conventional spectrum
estimation methods such as MUSIC from the estimated covariance matrix. Finally,
numerical examples are provided to validate the favorable performance of the
proposed algorithms, with comparisons against several existing approaches.Comment: 14 pages, 10 figure
Bayesian compressive sensing framework for spectrum reconstruction in Rayleigh fading channels
Compressive sensing (CS) is a novel digital signal processing technique that has found great interest in
many applications including communication theory and wireless communications. In wireless communications, CS
is particularly suitable for its application in the area of spectrum sensing for cognitive radios, where the complete
spectrum under observation, with many spectral holes, can be modeled as a sparse wide-band signal in the frequency
domain. Considering the initial works performed to exploit the benefits of Bayesian CS in spectrum sensing, the fading
characteristic of wireless communications has not been considered yet to a great extent, although it is an inherent feature
for all sorts of wireless communications and it must be considered for the design of any practically viable wireless system.
In this paper, we extend the Bayesian CS framework for the recovery of a sparse signal, whose nonzero coefficients follow
a Rayleigh distribution. It is then demonstrated via simulations that mean square error significantly improves when
appropriate prior distribution is used for the faded signal coefficients and thus, in turns, the spectrum reconstruction
improves. Different parameters of the system model, e.g., sparsity level and number of measurements, are then varied
to show the consistency of the results for different cases
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