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We study the ubiquitous super-resolution problem, in which one aims at localizing positive point sources in an image, blurred by the point spread function of the imaging device. To recover the point sources, we propose to solve a convex…

This paper addresses the positive semi-definite procrustes problem (PSDP). The PSDP corresponds to a least squares problem over the set of symmetric and semi-definite positive matrices. These kinds of problems appear in many applications…

Problem definition: A key challenge in supervised learning is data scarcity, which can cause prediction models to overfit to the training data and perform poorly out of sample. A contemporary approach to combat overfitting is offered by…

The observations in many applications consist of counts of discrete events, such as photons hitting a dector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model.…

In this second paper in a series dedicated to developing efficient numerical techniques for the deblurring Cosmic Microwave Background (CMB) maps, we consider the case of asymmetric point spread functions (PSF). Although conceptually this…

Existing nonconvex statistical optimization theory and methods crucially rely on the correct specification of the underlying "true" statistical models. To address this issue, we take a first step towards taming model misspecification by…

Propagating uncertainties introduced by chemical reaction rate parameters to high-fidelity numerical simulations of complex combustion devices is necessary to ascertain impact on computational predictions. However, the high cost of detailed…

Joint probability mass function (PMF) estimation is a fundamental machine learning problem. The number of free parameters scales exponentially with respect to the number of random variables. Hence, most work on nonparametric PMF estimation…

We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…

Diffusion models are extensively used for modeling image priors for inverse problems. We introduce \emph{Diff-Unfolding}, a principled framework for learning posterior score functions of \emph{conditional diffusion models} by explicitly…

We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…

In astronomy, upcoming space telescopes with wide-field optical instruments have a spatially varying point spread function (PSF). Specific scientific goals require a high-fidelity estimation of the PSF at target positions where no direct…

Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…

The development of signal unmixing algorithms is essential for leveraging multimodal datasets acquired through a wide array of scientific imaging technologies, including hyperspectral or time-resolved acquisitions. In experimental physics,…

The Point Spread Function (PSF) is a key figure of merit for specifying the angular resolution of optical systems and, as the demand for higher and higher angular resolution increases, the problem of surface finishing must be taken…

Recovering the turbulence-degraded point spread function from a single intensity image is important for a variety of imaging applications. Here, a deep learning model based on a convolutional neural network is applied to intensity images to…

Shape constraints, such as non-negativity, monotonicity, convexity or supermodularity, play a key role in various applications of machine learning and statistics. However, incorporating this side information into predictive models in a hard…

Hyperspectral (HS) unmixing is the process of decomposing an HS image into material-specific spectra (endmembers) and their spatial distributions (abundance maps). Existing unmixing methods have two limitations with respect to noise…

Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…

Localization microscopy enables imaging with resolutions that surpass the conventional optical diffraction limit. Notably, the MINFLUX method achieves super-resolution by shaping the excitation point-spread function (PSF) to minimize the…