185 research outputs found
Radiative Transfer Limits of Two-Frequency Wigner Distribution for Random Parabolic Waves
The present note establishes the self-averaging, radiative transfer limit for
the two-frequency Wigner distribution for classical waves in random media.
Depending on the ratio of the wavelength to the correlation length the limiting
equation is either a Boltzmann-like integral equation or a Fokker-Planck-like
differential equation in the phase space. The limiting equation is used to
estimate three physical parameters: the spatial spread, the coherence length
and the coherence bandwidth. In the longitudinal case, the Fokker-Planck-like
equation can be solved exactly.Comment: typos correcte
Compressive Sensing Theory for Optical Systems Described by a Continuous Model
A brief survey of the author and collaborators' work in compressive sensing
applications to continuous imaging models.Comment: Chapter 3 of "Optical Compressive Imaging" edited by Adrian Stern
published by Taylor & Francis 201
TV-min and Greedy Pursuit for Constrained Joint Sparsity and Application to Inverse Scattering
This paper proposes a general framework for compressed sensing of constrained
joint sparsity (CJS) which includes total variation minimization (TV-min) as an
example. TV- and 2-norm error bounds, independent of the ambient dimension, are
derived for the CJS version of Basis Pursuit and Orthogonal Matching Pursuit.
As an application the results extend Cand`es, Romberg and Tao's proof of exact
recovery of piecewise constant objects with noiseless incomplete Fourier data
to the case of noisy data.Comment: Mathematics and Mechanics of Complex Systems (2013
Richardson's Laws for Relative Dispersion in Colored-Noise Flows with Kolmogorov-type Spectra
We prove limit theorems for small-scale pair dispersion in velocity fields
with power-law spatial spectra and wave-number dependent correlation times.
This result establishes rigorously a family of generalized Richardson's laws
with a limiting case corresponding to Richardson's and 4/3-laws
Convergence of Passive Scalars in Ornstein-Uhlenbeck Flows to Kraichnan's Model
We prove that the passive scalar field in the Ornstein-Uhlenbeck velocity
field with wave-number dependent correlation times converges, in the
white-noise limit, to that of Kraichnan's model with higher spatial regularity
White-Noise and Geometrical Optics Limits of Wigner-Moyal Equation for Wave Beams in Turbulent Media
Starting with the Wigner distribution formulation for beam wave propagation
in H\"{o}lder continuous non-Gaussian random refractive index fields we show
that the wave beam regime naturally leads to the white-noise scaling limit and
converges to a Gaussian white-noise model which is characterized by the
martingale problem associated to a stochastic differential-integral equation of
the It\^o type. In the simultaneous geometrical optics the convergence to the
Gaussian white-noise model for the Liouville equation is also established if
the ultraviolet cutoff or the Fresnel number vanishes sufficiently slowly. The
advantage of the Gaussian white-noise model is that its -point correlation
functions are governed by closed form equations
Self-Averaged Scaling Limits for Random Parabolic Waves
We consider 6 types of scaling limits for the Wigner-Moyal equation of the
parabolic waves in random media, the limiting cases of which include the
radiative transfer limit, the diffusion limit and the white-noise limit. We
show under fairly general assumptions on the random refractive index field that
sufficient amount of medium diversity (thus excluding the white-noise limit)
leads to statistical stability or self-averaging in the sense that the limiting
law is deterministic and is governed by various transport equations depending
on the specific scaling involved. We obtain 6 different radiative transfer
equations as limits
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