37,624 research outputs found
Toeplitz-Structured Chaotic Sensing Matrix for Compressive Sensing
International audienceCompressive Sensing (CS) is a new sampling theory which allows signals to be sampled at sub-Nyquist rate without loss of information. Fundamentally, its procedure can be modeled as a linear projection on one specific sensing matrix, which, in order to guarantee the information conservation, satisfies Restricted Isometry Property (RIP). Ordinarily, this matrix is constructed by the Gaussian random matrix or Bernoulli random matrix. In previous work, we have proved that the typical chaotic sequence - logistic map can be adopted to generate the sensing matrix for CS. In this paper, we show that Toeplitz-structured matrix constructed by chaotic sequence is sufficient to satisfy RIP with high probability. With the Toeplitz-structured Chaotic Sensing Matrix (TsCSM), we can easily build a filter with small number of taps. Meanwhile, we implement the TsCSM in compressive sensing of images
Short-Pulsed Wavepacket Propagation in Ray-Chaotic Enclosures
Wave propagation in ray-chaotic scenarios, characterized by exponential
sensitivity to ray-launching conditions, is a topic of significant interest,
with deep phenomenological implications and important applications, ranging
from optical components and devices to time-reversal focusing/sensing schemes.
Against a background of available results that are largely focused on the
time-harmonic regime, we deal here with short-pulsed wavepacket propagation in
a ray-chaotic enclosure. For this regime, we propose a rigorous analytical
framework based on a short-pulsed random-plane-wave statistical representation,
and check its predictions against the results from
finite-difference-time-domain numerical simulations.Comment: 11 pages, 11 figures; minor modifications in the tex
Sensing Small Changes in a Wave Chaotic Scattering System
Classical analogs of the quantum mechanical concepts of the Loschmidt Echo
and quantum fidelity are developed with the goal of detecting small
perturbations in a closed wave chaotic region. Sensing techniques that employ a
one-recording-channel time-reversal-mirror, which in turn relies on time
reversal invariance and spatial reciprocity of the classical wave equation, are
introduced. In analogy with quantum fidelity, we employ Scattering Fidelity
techniques which work by comparing response signals of the scattering region,
by means of cross correlation and mutual information of signals. The
performance of the sensing techniques is compared for various perturbations
induced experimentally in an acoustic resonant cavity. The acoustic signals are
parametrically processed to mitigate the effect of dissipation and to vary the
spatial diversity of the sensing schemes. In addition to static boundary
condition perturbations at specified locations, perturbations to the medium of
wave propagation are shown to be detectable, opening up various real world
sensing applications in which a false negative cannot be tolerated.Comment: 14 pages, 11 figures, as published on J. Appl. Phy
Spatially Dependent Parameter Estimation and Nonlinear Data Assimilation by Autosynchronization of a System of Partial Differential Equations
Given multiple images that describe chaotic reaction-diffusion dynamics,
parameters of a PDE model are estimated using autosynchronization, where
parameters are controlled by synchronization of the model to the observed data.
A two-component system of predator-prey reaction-diffusion PDEs is used with
spatially dependent parameters to benchmark the methods described. Applications
to modelling the ecological habitat of marine plankton blooms by nonlinear data
assimilation through remote sensing is discussed
Compressive Sensing with Chaotic Sequence
International audienceCompressive sensing is a new methodology to cap- ture signals at sub-Nyquist rate. To guarantee exact recovery from compressed measurements, one should choose specific matrix, which satisfies the Restricted Isometry Property (RIP), to implement the sensing procedure. In this letter, we propose to construct the sensing matrix with chaotic sequence following a trivial method and prove that with overwhelming probability, the RIP of this kind of matrix is guaranteed. Meanwhile, its experimental comparisons with Gaussian random matrix, Bernoulli random matrix and sparse matrix are carried out and show that the performances among these sensing matrix are almost equal
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
Quantifying Volume Changing Perturbations in a Wave Chaotic System
A sensor was developed to quantitatively measure perturbations which change
the volume of a wave chaotic cavity while leaving its shape intact. The sensors
work in the time domain by using either scattering fidelity of the transmitted
signals or time reversal mirrors. The sensors were tested experimentally by
inducing volume changing perturbations to a one cubic meter mixed chaotic and
regular billiard system. Perturbations which caused a volume change that is as
small as 54 parts in a million were quantitatively measured. These results were
obtained by using electromagnetic waves with a wavelength of about 5cm,
therefore, the sensor is sensitive to extreme sub-wavelength changes of the
boundaries of a cavity. The experimental results were compared with Finite
Difference Time Domain (FDTD) simulation results, and good agreement was found.
Furthermore, the sensor was tested using a frequency domain approach on a
numerical model of the star graph, which is a representative wave chaotic
system. These results open up interesting applications such as: monitoring the
spatial uniformity of the temperature of a homogeneous cavity during heating up
/ cooling down procedures, verifying the uniform displacement of a fluid inside
a wave chaotic cavity by another fluid, etc.Comment: 13 pages, 13 figure
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