相关论文: Wasserstein-based Projections with Applications to…

Data consisting of time-indexed distributions of cross-sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions.…

Machine learning image classifiers are susceptible to adversarial and corruption perturbations. Adding imperceptible noise to images can lead to severe misclassifications of the machine learning model. Using $L_p$-norms for measuring the…

We present a Bayesian framework based on a new exponential likelihood function driven by the quadratic Wasserstien metric. Compared to conventional Bayesian models based on Gaussian likelihood functions driven by the least-squares norm…

Deep learning has recently demonstrated its excellent performance on the task of multi-view stereo (MVS). However, loss functions applied for deep MVS are rarely studied. In this paper, we first analyze existing loss functions' properties…

Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution. Many kinds of priors have been explored in the…

Plug-and-play (PnP) prior is a well-known class of methods for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image denoisers. While PnP methods have been…

A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…

Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as…

Uncertainty quantification is crucial to inverse problems, as it could provide decision-makers with valuable information about the inversion results. For example, seismic inversion is a notoriously ill-posed inverse problem due to the…

These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…

This paper builds on classical distributionally robust optimization techniques to construct a comprehensive framework that can be used for solving inverse problems. Given an estimated distribution of inputs in $X$ and outputs in $Y$, an…

In this paper, a statistically optimal solution to the Perspective-n-Point (PnP) problem is presented. Many solutions to the PnP problem are geometrically optimal, but do not consider the uncertainties of the observations. In addition, it…

Achieving high-quality Magnetic Resonance Imaging (MRI) reconstruction at accelerated acquisition rates remains challenging due to the inherent ill-posed nature of the inverse problem. Traditional Compressed Sensing (CS) methods, while…

Many application domains, spanning from computational photography to medical imaging, require recovery of high-fidelity images from noisy, incomplete or partial/compressed measurements. State of the art methods for solving these inverse…

Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…

In this work we compute lower Lipschitz bounds of $\ell_p$ pooling operators for $p=1, 2, \infty$ as well as $\ell_p$ pooling operators preceded by half-rectification layers. These give sufficient conditions for the design of invertible…

A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…

Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…

Plug-and-play (PnP) methods are widely used for solving imaging inverse problems by incorporating a denoiser into optimization algorithms. Score-based diffusion models (SBDMs) have recently demonstrated strong generative performance through…

Partially Observable Markov Decision Processes (POMDPs) are used to model environments where the full state cannot be perceived by an agent. As such the agent needs to reason taking into account the past observations and actions. However,…