10,456 research outputs found
Info-Greedy sequential adaptive compressed sensing
We present an information-theoretic framework for sequential adaptive
compressed sensing, Info-Greedy Sensing, where measurements are chosen to
maximize the extracted information conditioned on the previous measurements. We
show that the widely used bisection approach is Info-Greedy for a family of
-sparse signals by connecting compressed sensing and blackbox complexity of
sequential query algorithms, and present Info-Greedy algorithms for Gaussian
and Gaussian Mixture Model (GMM) signals, as well as ways to design sparse
Info-Greedy measurements. Numerical examples demonstrate the good performance
of the proposed algorithms using simulated and real data: Info-Greedy Sensing
shows significant improvement over random projection for signals with sparse
and low-rank covariance matrices, and adaptivity brings robustness when there
is a mismatch between the assumed and the true distributions.Comment: Preliminary results presented at Allerton Conference 2014. To appear
in IEEE Journal Selected Topics on Signal Processin
Joint Reconstruction of Absorbed Optical Energy Density and Sound Speed Distribution in Photoacoustic Computed Tomography: A numerical Investigation
Photoacoustic computed tomography (PACT) is a rapidly emerging bioimaging
modality that seeks to reconstruct an estimate of the absorbed optical energy
density within an object. Conventional PACT image reconstruction methods assume
a constant speed-of-sound (SOS), which can result in image artifacts when
acoustic aberrations are significant. It has been demonstrated that
incorporating knowledge of an object's SOS distribution into a PACT image
reconstruction method can improve image quality. However, in many cases, the
SOS distribution cannot be accurately and/or conveniently estimated prior to
the PACT experiment. Because variations in the SOS distribution induce
aberrations in the measured photoacoustic wavefields, certain information
regarding an object's SOS distribution is encoded in the PACT measurement data.
Based on this observation, a joint reconstruction (JR) problem has been
proposed in which the SOS distribution is concurrently estimated along with the
sought-after absorbed optical energy density from the photoacoustic measurement
data. A broad understanding of the extent to which the JR problem can be
accurately and reliably solved has not been reported. In this work, a series of
numerical experiments is described that elucidate some important properties of
the JR problem that pertain to its practical feasibility. To accomplish this,
an optimization-based formulation of the JR problem is developed that yields a
non-linear iterative algorithm that alternatingly updates the two image
estimates. Heuristic analytic insights into the reconstruction problem are also
provided. These results confirm the ill-conditioned nature of the joint
reconstruction problem that will present significant challenges for practical
applications.Comment: 13 pages, submitted to IEEE Transactions on Computational Imagin
Variational Bayesian Inference of Line Spectra
In this paper, we address the fundamental problem of line spectral estimation
in a Bayesian framework. We target model order and parameter estimation via
variational inference in a probabilistic model in which the frequencies are
continuous-valued, i.e., not restricted to a grid; and the coefficients are
governed by a Bernoulli-Gaussian prior model turning model order selection into
binary sequence detection. Unlike earlier works which retain only point
estimates of the frequencies, we undertake a more complete Bayesian treatment
by estimating the posterior probability density functions (pdfs) of the
frequencies and computing expectations over them. Thus, we additionally capture
and operate with the uncertainty of the frequency estimates. Aiming to maximize
the model evidence, variational optimization provides analytic approximations
of the posterior pdfs and also gives estimates of the additional parameters. We
propose an accurate representation of the pdfs of the frequencies by mixtures
of von Mises pdfs, which yields closed-form expectations. We define the
algorithm VALSE in which the estimates of the pdfs and parameters are
iteratively updated. VALSE is a gridless, convergent method, does not require
parameter tuning, can easily include prior knowledge about the frequencies and
provides approximate posterior pdfs based on which the uncertainty in line
spectral estimation can be quantified. Simulation results show that accounting
for the uncertainty of frequency estimates, rather than computing just point
estimates, significantly improves the performance. The performance of VALSE is
superior to that of state-of-the-art methods and closely approaches the
Cram\'er-Rao bound computed for the true model order.Comment: 15 pages, 8 figures, accepted for publication in IEEE Transactions on
Signal Processin
No More Pesky Learning Rates
The performance of stochastic gradient descent (SGD) depends critically on
how learning rates are tuned and decreased over time. We propose a method to
automatically adjust multiple learning rates so as to minimize the expected
error at any one time. The method relies on local gradient variations across
samples. In our approach, learning rates can increase as well as decrease,
making it suitable for non-stationary problems. Using a number of convex and
non-convex learning tasks, we show that the resulting algorithm matches the
performance of SGD or other adaptive approaches with their best settings
obtained through systematic search, and effectively removes the need for
learning rate tuning
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