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We consider the problem of imitation learning under misspecification: settings where the learner is fundamentally unable to replicate expert behavior everywhere. This is often true in practice due to differences in observation space and…
In super-resolution it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at low frequencies capped by f_c. In the case when the point sources are positive and are located on a…
This paper investigates the simultaneous identification of a spatially dependent potential and the initial condition in a subdiffusion model based on two terminal observations. The existence, uniqueness, and conditional stability of the…
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…
This paper focuses on characterizing the fundamental performance limits that can be expected from an ideal decoder given a general model, ie, a general subset of "simple" vectors of interest. First, we extend the so-called notion of…
The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…
We consider the sound ranging, or source localization, problem - find the source-point from the moments when the wave-sphere of linearly, with time, increasing radius reaches the sensor-points - in the proper metric spaces (any closed ball…
We consider the problem of audio voice separation for binaural applications, such as earphones and hearing aids. While today's neural networks perform remarkably well (separating $4+$ sources with 2 microphones) they assume a known or fixed…
We study theoretically light focusing at subwavelength scale inside a disordered strongly scattering open medium. We show that broadband time reversal at a single point antenna, in conjunction with near-field interactions and multiple…
This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…
Self-attention is a method of encoding sequences of vectors by relating these vectors to each-other based on pairwise similarities. These models have recently shown promising results for modeling discrete sequences, but they are non-trivial…
This paper is concerned with reconstructing an acoustic obstacle and its excitation sources from the phaseless near-field measurements. By supplementing some artificial sources to the inverse scattering system, this co-inversion problem can…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
We study the inverse conductivity problem with discontinuous conductivities. We consider, simultaneously, a regularisation and a discretisation for a variational approach to solve the inverse problem. We show that, under suitable choices of…
We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…
We study the fixed angle inverse scattering problem of determining a sound speed from scattering measurements corresponding to a single incident wave. The main result shows that a sound speed close to constant can be stably determined by…
In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic…
Self-supervised learning can significantly improve the performance of downstream tasks, however, the dimensions of learned representations normally lack explicit physical meanings. In this work, we propose a novel self-supervised approach…
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…