相关论文: Sparse super resolution is Lipschitz continuous

Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite…

In mathematics, a super-resolution problem can be formulated as acquiring high-frequency data from low-frequency measurements. This extrapolation problem in the frequency domain is well-known to be unstable. We propose a model-based…

The ability to resolve detail in the object that is being imaged, named by resolution, is the core parameter of an imaging system. Super-resolution is a class of techniques that can enhance the resolution of an imaging system and even…

This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is an off-the-grid generalisation of l1 regularization (also…

This paper establishes a general topological condition under which the semilocal stability of a set-valued mapping can be exactly determined by its local stability properties. Specifically, we investigate the relationship between the…

Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…

The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an…

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…

Image super-resolution remains an important research topic to overcome the limitations of physical acquisition systems, and to support the development of high resolution displays. Previous example-based super-resolution approaches mainly…

Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely…

Lipschitz constants of neural networks allow for guarantees of robustness in image classification, safety in controller design, and generalizability beyond the training data. As calculating Lipschitz constants is NP-hard, techniques for…

The Lipschitz constant is a key measure for certifying the robustness of neural networks to input perturbations. However, computing the exact constant is NP-hard, and standard approaches to estimate the Lipschitz constant involve solving a…

Beside the minimization of the prediction error, two of the most desirable properties of a regression scheme are stability and interpretability. Driven by these principles, we propose continuous-domain formulations for one-dimensional…

We study the geometry of the space of measures of a compact ultrametric space X, endowed with the L^p Wasserstein distance from optimal transportation. We show that the power p of this distance makes this Wasserstein space affinely…

This paper is motivated by structured sparsity for deep neural network training. We study a weighted group L0-norm constraint, and present the projection and normal cone of this set. Using randomized smoothing, we develop zeroth and…

The Lipschitz constant plays a crucial role in certifying the robustness of neural networks to input perturbations. Since calculating the exact Lipschitz constant is NP-hard, efforts have been made to obtain tight upper bounds on the…

Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…

We present a pursuit-like algorithm that we call the "superset method" for recovery of sparse vectors from consecutive Fourier measurements in the super-resolution regime. The algorithm has a subspace identification step that hinges on the…

This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…