4,043 research outputs found
Nonlinear Compressive Particle Filtering
Many systems for which compressive sensing is used today are dynamical. The
common approach is to neglect the dynamics and see the problem as a sequence of
independent problems. This approach has two disadvantages. Firstly, the
temporal dependency in the state could be used to improve the accuracy of the
state estimates. Secondly, having an estimate for the state and its support
could be used to reduce the computational load of the subsequent step. In the
linear Gaussian setting, compressive sensing was recently combined with the
Kalman filter to mitigate above disadvantages. In the nonlinear dynamical case,
compressive sensing can not be used and, if the state dimension is high, the
particle filter would perform poorly. In this paper we combine one of the most
novel developments in compressive sensing, nonlinear compressive sensing, with
the particle filter. We show that the marriage of the two is essential and that
neither the particle filter or nonlinear compressive sensing alone gives a
satisfying solution.Comment: Accepted to CDC 201
Norm minimized Scattering Data from Intensity Spectra
We apply the minimizing technique of compressive sensing (CS) to
non-linear quadratic observations. For the example of coherent X-ray scattering
we provide the formulae for a Kalman filter approach to quadratic CS and show
how to reconstruct the scattering data from their spatial intensity
distribution.Comment: 26 pages, 10 figures, reordered section
Analyzing Least Squares and Kalman Filtered Compressed Sensing
In recent work, we studied the problem of causally reconstructing time
sequences of spatially sparse signals, with unknown and slow time-varying
sparsity patterns, from a limited number of linear "incoherent" measurements.
We proposed a solution called Kalman Filtered Compressed Sensing (KF-CS). The
key idea is to run a reduced order KF only for the current signal's estimated
nonzero coefficients' set, while performing CS on the Kalman filtering error to
estimate new additions, if any, to the set. KF may be replaced by Least Squares
(LS) estimation and we call the resulting algorithm LS-CS. In this work, (a) we
bound the error in performing CS on the LS error and (b) we obtain the
conditions under which the KF-CS (or LS-CS) estimate converges to that of a
genie-aided KF (or LS), i.e. the KF (or LS) which knows the true nonzero sets.Comment: Proc. IEEE Intl. Conf. Acous. Speech Sig. Proc. (ICASSP), 200
Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing
In this work the dynamic compressive sensing (CS) problem of recovering
sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear
measurements is explored from a Bayesian perspective. While there has been a
handful of previously proposed Bayesian dynamic CS algorithms in the
literature, the ability to perform inference on high-dimensional problems in a
computationally efficient manner remains elusive. In response, we propose a
probabilistic dynamic CS signal model that captures both amplitude and support
correlation structure, and describe an approximate message passing algorithm
that performs soft signal estimation and support detection with a computational
complexity that is linear in all problem dimensions. The algorithm, DCS-AMP,
can perform either causal filtering or non-causal smoothing, and is capable of
learning model parameters adaptively from the data through an
expectation-maximization learning procedure. We provide numerical evidence that
DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety
of operating conditions. We further describe the result of applying DCS-AMP to
two real dynamic CS datasets, as well as a frequency estimation task, to
bolster our claim that DCS-AMP is capable of offering state-of-the-art
performance and speed on real-world high-dimensional problems.Comment: 32 pages, 7 figure
Exploiting flow dynamics for super-resolution in contrast-enhanced ultrasound
Ultrasound localization microscopy offers new radiation-free diagnostic tools
for vascular imaging deep within the tissue. Sequential localization of echoes
returned from inert microbubbles with low-concentration within the bloodstream
reveal the vasculature with capillary resolution. Despite its high spatial
resolution, low microbubble concentrations dictate the acquisition of tens of
thousands of images, over the course of several seconds to tens of seconds, to
produce a single super-resolved image. %since each echo is required to be well
separated from adjacent microbubbles. Such long acquisition times and stringent
constraints on microbubble concentration are undesirable in many clinical
scenarios. To address these restrictions, sparsity-based approaches have
recently been developed. These methods reduce the total acquisition time
dramatically, while maintaining good spatial resolution in settings with
considerable microbubble overlap. %Yet, non of the reported methods exploit the
fact that microbubbles actually flow within the bloodstream. % to improve
recovery. Here, we further improve sparsity-based super-resolution ultrasound
imaging by exploiting the inherent flow of microbubbles and utilize their
motion kinematics. While doing so, we also provide quantitative measurements of
microbubble velocities. Our method relies on simultaneous tracking and
super-localization of individual microbubbles in a frame-by-frame manner, and
as such, may be suitable for real-time implementation. We demonstrate the
effectiveness of the proposed approach on both simulations and {\it in-vivo}
contrast enhanced human prostate scans, acquired with a clinically approved
scanner.Comment: 11 pages, 9 figure
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