Related papers: Approximation by refinement masks
We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
In this paper we study the general reconstruction of a compactly supported function from its Fourier coefficients using compactly supported shearlet systems. We assume that only finitely many Fourier samples of the function are accessible…
We find asymptotic equalities for exact upper bounds of approximations by Fourier sums in uniform metric on classes of $2\pi$-periodic functions, representable in the form of convolutions of functions $\varphi$, which belong to unit balls…
We consider approximating analytic functions on the interval $[-1,1]$ from their values at a set of $m+1$ equispaced nodes. A result of Platte, Trefethen \& Kuijlaars states that fast and stable approximation from equispaced samples is…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
We consider the problem of approximation of a continuous function $f$ defined on a compact metric space $X$ by elements from a sum of two algebras. We prove a de la Vall\'{e}e Poussin type theorem, which estimates the approximation error…
Two scaling functions $\varphi_A$ and $\varphi_B$ for Parseval frame wavelets are algebraically isomorphic, $\varphi_A \simeq \varphi_B$, if they have matching solutions to their (reduced) isomorphic systems of equations. Let $A$ and $B$ be…
We present in this paper a rigorous theoretical framework to show stability, convergence and accuracy of improved edge-based and face-based smoothed finite element methods (bESFEM and bFS-FEM) for nearly-incompressible elasticity problems.…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
This paper offers a new regard on compactly supported wavelets derived from FIR filters. Although being continuous wavelets, analytical formulation are lacking for such wavelets. Close approximations for daublets (Daubechies wavelets) and…
We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…
Functions in a Sobolev space are approximated directly by piecewise affine interpolation in the norm of the space. The proof is based on estimates for interpolations and does not rely on the density of smooth functions.
Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these…
In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution…
It is described how the coefficients of Daubechies wavelet matrices can be approximated by rational numbers in such a way that the perfect reconstruction property of the filter bank be preserved exactly
This paper is devoted to the study of a problem of Cassels in multiplicative Diophantine approximation which involves minimising values of a product of affine linear forms computed at integral points. It was previously known that values of…
For any symmetry group $H$ and any appropriate matrix dilation we give an explicit method for the construction of $H$-symmetric refinable interpolatory refinable masks which satisfy sum rule of arbitrary order $n$. For each such mask we…
In order to have a multiresolution analysis, the scaling function must be refinable. That is, it must be the linear combination of 2-dilation, $\mathbb{Z}$-translates of itself. Refinable functions used in connection with wavelets are…
Continuing our recent work we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider such polynomial masks that are derived by means of the…