Related papers: Towards a Theory of Stable Super-Resolution: Model…
We develop a multidimensional version of Gradient-MUSIC for estimating the frequencies of a nonharmonic signal from noisy samples. The guiding principle is that frequency recovery should be based only on the signal subspace determined by…
This work investigates the stability of (discrete) empirical interpolation for nonlinear model reduction and state field approximation from measurements. Empirical interpolation derives approximations from a few samples (measurements) via…
Super-resolution (SR) models are attracting growing interest for enhancing minimally invasive surgery and diagnostic videos under hardware constraints. However, valid concerns remain regarding the introduction of hallucinated structures and…
Particle tracking in biological imaging is concerned with reconstructing the trajectories, locations, or velocities of the targeting particles. The standard approach of particle tracking consists of two steps: first reconstructing…
This paper deals with the problem of reconstructing a band-limited signal when a finite subset of its samples and of its derivative are missing. The technique used, due to P.J.S.G. Ferreira, is based on the use of a particular frame for…
In this paper, we study a practical space-time video super-resolution (STVSR) problem which aims at generating a high-framerate high-resolution sharp video from a low-framerate low-resolution blurry video. Such problem often occurs when…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…
We propose a novel deep-learning framework for super-resolution ultrasound images and videos in terms of spatial resolution and line reconstruction. We up-sample the acquired low-resolution image through a vision-based interpolation method;…
The objective of image super-resolution is to reconstruct a high-resolution (HR) image with the prior knowledge from one or several low-resolution (LR) images. However, in the real world, due to the limited complementary information, the…
In frequency-limited model order reduction, the objective is to maintain the frequency response of the original system within a specified frequency range in the reduced-order model. In this paper, a mathematical expression for the…
Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications,…
In this paper, we show the increasing stability of the inverse source problems for the acoustic wave equation in the full space R3.The goal is to understand increasing stability for wave equation in the time domain. If the time and spatial…
Reconstructive spectrometers are a promising emerging class of devices that combine complex light scattering with inference to enable compact, high-resolution spectrometry. Thus far, the physical determinants of these devices' performance…
In this paper, we will study increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain $\Omega$ with sufficiently smooth…
We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…
The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. H\"older or Lipschitz dependence of the optimal solution on perturbations are obtained for…
High resolution magnetic resonance~(MR) imaging~(MRI) is desirable in many clinical applications, however, there is a trade-off between resolution, speed of acquisition, and noise. It is common for MR images to have worse through-plane…
Reproducibility is imperative for any scientific discovery. More often than not, modern scientific findings rely on statistical analysis of high-dimensional data. At a minimum, reproducibility manifests itself in stability of statistical…
We consider the problem of estimating the parameters of a linear univariate autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze…