A numerical solution of diffraction problems for the radiation transport equation.
A two-dimensional inverse heat conduction problem for estimating heat source.
Algorithm for reconstruction of the elastic constants of an anisotropic layer lying in an isotropic horizontally stratified medium.
Introduction to magnetic resonance imaging for mathematicians
The basic concepts and models used in the study of nuclear magnetic resonance are introduced. A simple imaging experiment is described, as well as, the reduction of the problem of selective excitation to a classical problem in inverse scattering.
Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data
We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to...
Minimax and bayes estimation in deconvolution problem*
We consider a deconvolution problem of estimating a signal blurred with a random noise. The noise is assumed to be a stationary Gaussian process multiplied by a weight function function εh where h ∈ L2(R1) and ε is a small parameter. The underlying solution is assumed to be infinitely differentiable. For this model we find asymptotically minimax and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii,...
Multichannel deblurring of digital images
Blur is a common problem that limits the effective resolution of many imaging systems. In this article, we give a general overview of methods that can be used to reduce the blur. This includes the classical multi-channel deconvolution problems as well as challenging extensions to spatially varying blur. The proposed methods are formulated as energy minimization problems with specific regularization terms on images and blurs. Experiments on real data illustrate very good and stable performance of...
Numerical linear algebra for nonlinear microwave imaging.
Numerical treatment of a time dependent inverse problem in photon transport
The time-dependent intensity of a UV-photon source, located inside an interstellar cloud, is determined by formulating and solving an inverse problem for the integro-differential transport equation of photons in a one-dimensional slab. Starting from a discretizazion of the forward problem, an iterative procedure is used to compute the values of the source intensity at increasing values of the time.
Semi-convergence and relaxation parameters for a class of SIRT algorithms.
Simple square smoothing regularization operators.