Related papers: Sparse super resolution is Lipschitz continuous
We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This…
Important research efforts have focused on the design and training of neural networks with a controlled Lipschitz constant. The goal is to increase and sometimes guarantee the robustness against adversarial attacks. Recent promising…
In this paper, we approach the task of determining sensitivity bounds for pose estimation neural networks. This task is particularly challenging as it requires characterizing the sensitivity of 3D rotations. We develop a sensitivity measure…
We consider Lipschitz maps with values in quasi-metric spaces and extend such maps to finitely many points. We prove that in this context every 1-Lipschitz map admits an extension such that its Lipschitz constant is bounded from above by…
Super-resolution imaging using sub-diffraction field localization by micron sized transparent beads (microspheres) was recently demonstrated [1]. Practical applications in microscopy require control over the positioning of the microspheres.…
The scanning electron microscope (SEM) produces an image of a sample by scanning it with a focused beam of electrons. The electrons interact with the atoms in the sample, which emit secondary electrons that contain information about the…
We prove the convergence, in the small mass limit, of statistically invariant states for a class of semi-linear damped wave equations, perturbed by an additive Gaussian noise, both with Lipschitz-continuous and with polynomial…
Terahertz time-domain spectroscopy (THz-TDS) employs sub-picosecond pulses to probe dielectric properties of materials giving as a result a 3-dimensional hyperspectral data cube. The spatial resolution of THz images is primarily limited by…
Sparse graphs built by sparse representation has been demonstrated to be effective in clustering high-dimensional data. Albeit the compelling empirical performance, the vanilla sparse graph ignores the geometric information of the data by…
Complex signed measures of finite total variation are a powerful signal model in many applications. Restricting to the $d$-dimensional torus, finitely supported measures allow for exact recovery if the trigonometric moments up to some order…
In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity. In…
With the advent of microsphere assisted microscopy in 2011, this technique emerged as a simple and easy way to obtain optical super-resolution. Although the possible mechanisms of imaging by microspheres are debated in the literature, most…
Common measures of neural representational (dis)similarity are designed to be insensitive to rotations and reflections of the neural activation space. Motivated by the premise that the tuning of individual units may be important, there has…
In this paper, we show that harmonic Bloch mappings are Lipschitz continuous with respect to the pseudo-hyperbolic metric. This result improves the corresponding result of Theorem 1 of [P. Ghatage, J. Yan, and D. Zheng, Composition…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
In single-molecule microscopy it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at frequencies capped by $f_c$, which is just about the frequency of natural light. This paper…
Improvement of label-free far-field resolution of optical imaging is possible with prior knowledge of the object such as its sparsity or accumulated by a posteriori examination of a similar class of object1-4. We show that the sole…
A new (unadjusted) Langevin Monte Carlo (LMC) algorithm with improved rates in total variation and in Wasserstein distance is presented. All these are obtained in the context of sampling from a target distribution $\pi$ that has a density…
The proliferation of large data sets and Bayesian inference techniques motivates demand for better data sparsification. Coresets provide a principled way of summarizing a large dataset via a smaller one that is guaranteed to match the…
This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed $\ell^2$ Lipschitz bounds, i.e. limited sensitivity to input perturbations. The Lipschitz guarantees are…