Related papers: Probabilistic approach to limited-data computed to…

Reconstructing lens potentials and lensed sources can easily become an underconstrained problem, even when the degrees of freedom are low, due to degeneracies, particularly when potential perturbations superimposed on a smooth lens are…

Ultrasound reflection tomography is widely used to image large complex specimens that are only accessible from a single side, such as well systems and nuclear power plant containment walls. Typical methods for inverting the measurement rely…

Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…

Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…

This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear),…

Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…

Sparse-view computed tomography (CT) is an effective method to reduce the radiation exposure in medical imaging. To reduce the severe streaking artifacts that occur in reconstructed images due to violation of the Nyquist/Shannon sampling…

Shape constrained regression analysis has applications in dose-response modeling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid…

This paper presents an iterative inversion algorithm for computed tomography image reconstruction that performs well in terms of accuracy and speed using limited data. The computational method combines an image domain technique and…

We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…

We investigate a variational method for ill-posed problems, named $\texttt{graphLa+}\Psi$, which embeds a graph Laplacian operator in the regularization term. The novelty of this method lies in constructing the graph Laplacian based on a…

In this paper, we consider the problem of recovering compressively sensed ultrasound images. We build on prior work, and consider a number of existing approaches that we consider to be the state-of-the-art. The methods we consider take…

One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary…

We describe and examine an algorithm for tomographic image reconstruction where prior knowledge about the solution is available in the form of training images. We first construct a nonnegative dictionary based on prototype elements from the…

A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize…

Beamforming in ultrasound imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum is still extensively used nowadays in…

X-ray tomography is capable of imaging the interior of objects in three dimensions non-invasively, with applications in biomedical imaging, materials science, electronic inspection, and other fields. The reconstruction process can be an…

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…

X-ray tomography has been studied in various fields. Although a great deal of effort has been directed at reconstructing the projection image set from a rigid-type specimen, little attention has been addressed to the reconstruction of…

Recent research in tomographic reconstruction is motivated by the need to efficiently recover detailed anatomy from limited measurements. One of the ways to compensate for the increasingly sparse sets of measurements is to exploit the…