Related papers: Approximal operator with application to audio inpa…
Operator learning, the approximation of mappings between infinite-dimensional function spaces using machine learning, has gained increasing research attention in recent years. Approximate operators, learned from data, can serve as efficient…
Sasaki et al. (2018) presented an efficient audio declipping algorithm, based on the properties of Hankel-structure matrices constructed from time-domain signal blocks. We adapt their approach to solving the audio inpainting problem, where…
This work introduces the use of the Koopman operator theory to generate approximate analytical solutions for the zonal harmonics problem of a satellite orbiting a non-spherical celestial body. Particularly, the solution proposed directly…
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…
We consider the well-studied problem of decomposing a vector time series signal into components with different characteristics, such as smooth, periodic, nonnegative, or sparse. We describe a simple and general framework in which the…
Given an input sound signal and a target virtual sound source, sound spatialisation algorithms manipulate the signal so that a listener perceives it as though it were emitted from the target source. There exist several established…
The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…
We show that the expected solution operator of prototypical linear elliptic partial differential operators with random coefficients is well approximated by a computable sparse matrix. This result is based on a random localized orthogonal…
The parameters of a neural network are naturally organized in groups, some of which might not contribute to its overall performance. To prune out unimportant groups of parameters, we can include some non-differentiable penalty to the…
Given an operator ideal I, a Banach space E has the I-approximation property if operators on E can be uniformly approximated on compact subsets of E by operators belonging to I. In this paper the I- approximation property is studied in…
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…
This paper considers the problem of approximating the inverse of the wave-equation Hessian, also called normal operator, in seismology and other types of wave-based imaging. An expansion scheme for the pseudodifferential symbol of the…
Recently, great attention was intended toward overcomplete dictionaries and the sparse representations they can provide. In a wide variety of signal processing problems, sparsity serves a crucial property leading to high performance.…
We make several contributions to our recent program investigating structural properties of algebras of operators on a Hilbert space. For example, we make substantial contributions to the noncommutative peak interpolation program begun by…
We obtain estimates in simultaneous approximation for a summation-integral type genuine hybrid operator. The convergence of derivatives of operator to the corresponding derivatives of the functions is proved and estimates for rate of…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
We introduce computable projection operators onto piecewise polynomial spaces, defined via sampling and discrete least-squares polynomial approximations. The resulting mappings exhibit (almost) optimal approximation properties in $L^2$ and…
Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…
We prove sharp Lieb-Thirring type inequalities for the eigenvalues of a class of one-dimensional functional difference operators associated to mirror curves. We furthermore prove that the bottom of the essential spectrum of these operators…
This paper aims to develop new and fast algorithms for recovering a sparse vector from a small number of measurements, which is a fundamental problem in the field of compressive sensing (CS). Currently, CS favors incoherent systems, in…