相关论文: A solution to the inverse problem of non-coherent …

The existing description of non-coherent wave field propagation in terms of Fourier transformation has made possible to prove non-existence of the self-imaging phenomenon for non-coherent images.

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…

We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…

The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…

Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…

A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…

The nonlinear propagation of intense incoherent photons in a photon gas is considered. The photon-photon interactions are governed by a pair of equations comprising a wave-kinetic equation for the incoherent photons in the presence of the…

Motivated by applications in imaging nonlinear optical absorption by photoacoustic tomography (PAT), we study in this work inverse coefficient problems for a semilinear radiative transport equation and its diffusion approximation with…

This paper presents an uncalibrated deep neural network framework for the photometric stereo problem. For training models to solve the problem, existing neural network-based methods either require exact light directions or ground-truth…

We study the use of a learned forward operator in the inverse problem of photoacoustic tomography. The Fourier neural operator to approximate the photoacoustic wave propagation is used. Further, the inverse problem is solved using a…

We consider the propagation of both fully coherent and partially coherent complex scalar fields, through linear shift-invariant imaging systems. The state of such imaging systems is characterized by a countable infinity of aberration…

We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…

A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…

We propose a scheme for imaging periodic surfaces using a superlens. By employing an inverse scattering model and the transformed field expansion method, we derive an approximate reconstruction formula for the surface profile, assuming…

This paper proposes a neural network approach for solving two classical problems in the two-dimensional inverse wave scattering: far field pattern problem and seismic imaging. The mathematical problem of inverse wave scattering is to…

This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…

In this paper, an inverse variational problem is solved for the nonlocal nonlinear Schrdinger equation used in modeling filamentation in various nonlinear media. The corresponding integral relations are found which generalize the…

We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…

Inverse scattering is a fundamental challenge in many imaging applications, ranging from microscopy to remote sensing. Solving this problem often requires jointly estimating two unknowns -- the image and the scattering field inside the…

We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.