Related papers: Non-linearity in monochromatic transmission tomogr…
In this article, we are concerned with a nonlinear inverse problem with a forward operator involving an unknown function. The problem arises in diverse applications and is challenging in the presence of an unknown function, which makes it…
X-ray scattering patterns from emerging single particle experiments have commonly many missing or contaminated pixels. This complicates different analyses including projections on Fourier or other basis functions (for noise suppression,…
We consider the ultrasound imaging problem governed by a nonlinear wave equation of Westervelt type with variable wave speed. We show that the coefficient of nonlinearity can be recovered uniquely from knowledge of the Dirichlet-to-Neumann…
Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…
We have observed nonlinear transduction of the thermomechanical motion of a nanomechanical resonator when detected as laser transmission through a sideband unresolved optomechanical cavity. Nonlinear detection mechanisms are of considerable…
Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as…
Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…
Photodetector nonlinearity, the main limiting factor in terms of optical power in the detection chain, is corrected to improve the signal-to-noise ratio of a short-time measurement in dual-comb spectroscopy. An iterative correction…
We consider in a two dimensional absorbing and scattering medium, an inverse source problem in the stationary radiative transport, where the source is linearly anisotropic. The medium has an anisotropic scattering property that is neither…
We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…
In vision science, cascades of Linear+Nonlinear transforms are very successful in modeling a number of perceptual experiences [Carandini&Heeger12]. However, the conventional literature is usually too focused on only describing the…
This paper analyzes the nonlinear correspondence between the reflectivity profile (model) and the plane wave impulse response at the boundary (data) for a three-dimensional half space consisting of a sequence of homogeneous horizontal…
We study transport properties of an array created by alternating $(a,b)$ layers with balanced loss/gain characterized by the key parameter $\gamma$. It is shown that for non-equal widths of $(a,b)$ layers, i.e., when the corresponding…
We study coherent backscattering of a quasi-monochromatic laser by a dilute gas of cold two-level atoms. We consider the perturbative regime of weak intensities, where nonlinear effects arise from {\em inelastic} two-photon scattering…
Linear optical networks are fundamental to the advancement of quantum technologies, including quantum computing, communication, and sensing. The accurate characterization of these networks, described by unitary matrices, is crucial to their…
While nonlinear optical spectroscopy is becoming more commonly used to study the excited states of nonlinear-optical systems, a general theory of inhomogeneous broadening is rarely applied in lieu of either a simple Lorentzian or Gaussian…
In this article, we demonstrate the viability of highly monochromatic full-field X-ray absorption near edge structure based tomography using a laboratory-scale Johann-type X-ray absorption spectrometer based on a conventional X-ray tube…
Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…
Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…
The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively…