Related papers: Rapid and facile reconstruction of time-resolved f…
In this paper, we characterize data-time tradeoffs of the proximal-gradient homotopy method used for solving linear inverse problems under sub-Gaussian measurements. Our results are sharp up to an absolute constant factor. We demonstrate…
We study the task of noiseless linear regression under Gaussian covariates in the presence of additive oblivious contamination. Specifically, we are given i.i.d.\ samples from a distribution $(x, y)$ on $\mathbb{R}^d \times \mathbb{R}$ with…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
In this paper, we consider the problem of feature reconstruction from incomplete x-ray CT data. Such problems occurs, e.g., as a result of dose reduction in the context medical imaging. Since image reconstruction from incomplete data is a…
In the phase retrieval problem, an unknown vector is to be recovered given quadratic measurements. This problem has received considerable attention in recent times. In this paper, we present an algorithm to solve a nonconvex formulation of…
Richardson-Lucy deconvolution is widely used to restore images from degradation caused by the broadening effects of a point spread function and corruption by photon shot noise, in order to recover an underlying object. In practice, this is…
We study a time-varying Bayesian optimization problem with bandit feedback, where the reward function belongs to a Reproducing Kernel Hilbert Space (RKHS). We approach the problem via an upper-confidence bound Gaussian Process algorithm,…
This paper investigates a recursive formulation of auto-regressive multi-fidelity Gaussian process regression in the challenging setting of noisy and non-nested high- and low-fidelity data. We propose a decoupled optimization strategy based…
We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These…
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…
The recently developed globally convergent numerical method for an inverse medium problem for the Helmholtz equation is tested on experimental data. The data were originally collected in the time domain, whereas the method works in the…
This paper concerns the numerical resolution of a data completion problem for the time-harmonic Maxwell equations in the electric field. The aim is to recover the missing data on the inaccessible part of the boundary of a bounded domain…
This paper introduces a new series of methods which combine modal decomposition algorithms, such as singular value decomposition and high-order singular value decomposition, and deep learning architectures to repair, enhance, and increase…
Information about microscopic objects with features smaller than the diffraction limit is almost entirely lost in a far-field diffraction image but could be partly recovered with data completition techniques. Any such approach critically…
A simple least-squares optimisation enables the determination of the spectrum for irregularly sampled data that is readily reconstructed using an adjoint transformation of the Non-Uniform Fast Fourier Transform (NFFT). This is an…
Recovering high-resolution structural and compositional information from coherent X-ray measurements involves solving coupled, nonlinear, and ill-posed inverse problems. Ptychography reconstructs a complex transmission function from…
A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called harmonic Gaussian…
Let $(Y_i,\theta_i)$, $i=1,...,n$, be independent random vectors distributed like $(Y,\theta) \sim G^*$, where the marginal distribution of $\theta$ is completely unknown, and the conditional distribution of $Y$ conditional on $\theta$ is…
The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…
Common workflows in machine learning and statistics rely on the ability to partition the information in a data set into independent portions. Recent work has shown that this may be possible even when conventional sample splitting is not…