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We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad…
This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method…
We introduce the sparse direct sampling method (DSM) to estimate properties of a region from signals that probe the region. We demonstrate the sparse-DSM on two separate problems: estimating both the angle-of-arrival of a radio wave…
The episodic, irregular and asynchronous nature of medical data render them difficult substrates for standard machine learning algorithms. We would like to abstract away this difficulty for the class of time-stamped categorical variables…
A procedure for unfolding the true distribution from experimental data is presented. Machine learning methods are applied for simultaneous identification of an apparatus function and solving of an inverse problem. A priori information about…
In image editing employing diffusion models, it is crucial to preserve the reconstruction fidelity to the original image while changing its style. Although existing methods ensure reconstruction fidelity through optimization, a drawback of…
This paper is concerned with the electromagnetic inverse scattering problem that aims to determine the location and shape of anisotropic scatterers from far field data (at a fixed frequency). We study the orthogonality sampling method which…
We study the inverse problem of locating point sources from far-field data under plane wave incidence. A direct computational method is developed based on multiple scattering theory, using a novel indicator function to avoid iterative…
We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse…
The point spread function (PSF) of a translation invariant imaging system is its impulse response, which cannot always be measured directly. This is the case in high energy X-ray radiography, and it must be estimated from images of…
The muon radiography technique is part of the straight-ray scanning imaging methods and it is usually employed to produce two-dimensional images of the integrated density in the radial direction from the detector position. However, in the…
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…
Diffusion probabilistic models (DPMs) are a key component in modern generative models. DPM-solvers have achieved reduced latency and enhanced quality significantly, but have posed challenges to find the exact inverse (i.e., finding the…
Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…
Direct imaging methods recover the presence, position, and shape of the unknown obstacles in time-harmonic inverse scattering without a priori knowledge of either the physical properties or the number of disconnected components of the…
Reconstructing high-fidelity magnetic resonance (MR) images from under-sampled k-space is a commonly used strategy to reduce scan time. The posterior sampling of diffusion models based on the real measurement data holds significant promise…
Diffusion models are a remarkably effective way of learning and sampling from a distribution $p(x)$. In posterior sampling, one is also given a measurement model $p(y \mid x)$ and a measurement $y$, and would like to sample from $p(x \mid…
The direct sampling method proposed by Walker et al. (JCGS 2011) can generate draws from weighted distributions possibly having intractable normalizing constants. The method may be of interest as a useful tool in situations which require…
Tomographic imaging is in general an ill-posed inverse problem. Typically, a single regularized image estimate of the sought-after object is obtained from tomographic measurements. However, there may be multiple objects that are all…
Since the dawn of scanning probe microscopy (SPM), tapping or intermittent contact mode has been one of the most widely used imaging modes. Manual optimization of tapping mode not only takes a lot of instrument and operator time, but also…