Related papers: Model-agnostic super-resolution in high dimensions
Denoising diffusion models are a recent class of generative models exhibiting state-of-the-art performance in image and audio synthesis. Such models approximate the time-reversal of a forward noising process from a target distribution to a…
High-dimensional inference refers to problems of statistical estimation in which the ambient dimension of the data may be comparable to or possibly even larger than the sample size. We study an instance of high-dimensional inference in…
Generative networks have experienced great empirical successes in distribution learning. Many existing experiments have demonstrated that generative networks can generate high-dimensional complex data from a low-dimensional easy-to-sample…
A new type of robust estimation problem is introduced where the goal is to recover a statistical model that has been corrupted after it has been estimated from data. Methods are proposed for "repairing" the model using only the design and…
We propose a methodology that exploits large and diverse data sets to accurately estimate the ambient medium's Green's functions in strongly scattering media. Given these estimates, obtained with and without the use of neural networks,…
We study the problem of super-resolution of a linear combination of Dirac distributions and their derivatives on a one-dimensional circle from noisy Fourier measurements. Following numerous recent works on the subject, we consider the…
The ability to determine precisely the separation of two frequencies is fundamental to spectroscopy, yet the resolution limit poses a critical challenge: distinguishing two incoherent signals becomes impossible when their frequencies are…
We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been recently shown that exact recovery is possible by…
Unlinked regression, in which covariates and responses are observed separately without known correspondence, has recently gained increasing attention. Deconvolution, on the other hand, is a fundamental and challenging problem in…
Phaseless super-resolution is the problem of recovering an unknown signal from measurements of the magnitudes of the low frequency Fourier transform of the signal. This problem arises in applications where measuring the phase, and making…
Score-based Generative Models (SGMs) approximate a data distribution by perturbing it with Gaussian noise and subsequently denoising it via a learned reverse diffusion process. These models excel at modeling complex data distributions and…
Several applications require the super-resolution of noisy images and the preservation of geometrical and texture features. State-of-the-art super-resolution methods do not account for noise and generally enhance the output image's…
We consider the limits of super-resolution using imaging constraints. Due to various theoretical and practical limitations, reconstruction-based methods have been largely restricted to small increases in resolution. In addition, motion-blur…
We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. This problem arises broadly across algorithms, statistics, and machine learning. By leveraging 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),…
We consider the inverse problem of recovering the locations and amplitudes of a collection of point sources represented as a discrete measure, given $M+1$ of its noisy low-frequency Fourier coefficients. Super-resolution refers to a stable…
Super-resolution using deep neural networks typically relies on highly curated training sets that are often unavailable in clinical deployment scenarios. Using loss functions that assume Gaussian-distributed residuals makes the learning…
High-resolution diffusion tensor imaging (DTI) is beneficial for probing tissue microstructure in fine neuroanatomical structures, but long scan times and limited signal-to-noise ratio pose significant barriers to acquiring DTI at…
The sparse layouts of radio interferometers result in an incomplete sampling of the sky in Fourier space which leads to artifacts in the reconstructed images. Cleaning these systematic effects is essential for the scientific use of…
We study the reknown deconvolution problem of recovering a distribution function from independent replicates (signal) additively contaminated with random errors (noise), whose distribution is known. We investigate whether a Bayesian…