Related papers: Adaptive non-uniform B-spline dictionaries on a co…
Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a…
Box splines provide smooth spline spaces as shifts of a single generating function on a lattice and so generalize tensor-product splines. Their elegant theory is laid out in classical papers and a summarizing book. This compendium aims to…
This work introduces and analyzes B-spline approximation spaces defined on general geometric domains obtained through a mapping from a parameter domain. These spaces are constructed as sparse-grid tensor products of univariate spaces in the…
There are many significant applied contexts that require the solution of discontinuous optimization problems in finite dimensions. Yet these problems are very difficult, both computationally and analytically. With the functions being…
Multi-degree splines are smooth piecewise-polynomial functions where the pieces can have different degrees. We describe a simple algorithmic construction of a set of basis functions for the space of multi-degree splines, with similar…
In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral…
In this paper, it is proved that dictionary learning and sparse representation is invariant to a linear transformation. It subsumes the special case of transforming/projecting the data into a discriminative space. This is important because…
We consider a class of non-polynomial spline spaces over T-meshes, that is, of spaces locally spanned both by polynomial and by suitably-chosen non-polynomial functions, which we will refer to as generalized splines over T-meshes. For such…
Many applications like audio and image processing show that sparse representations are a powerful and efficient signal modeling technique. Finding an optimal dictionary that generates at the same time the sparsest representations of data…
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent…
This paper deals with Hermite osculatory interpolating splines. For a partition of a real interval endowed with a refinement consisting in dividing each subinterval into two small subintervals, we consider a space of smooth splines with…
This document facilitates understanding of core concepts about uniform B-spline and its matrix representation.
Inspired by shape constrained estimation under general nonnegative derivative constraints, this paper considers the B-spline approximation of constrained functions and studies the asymptotic performance of the constrained B-spline…
In this paper, we introduce a wideband dictionary framework for estimating sparse signals. By formulating integrated dictionary elements spanning bands of the considered parameter space, one may efficiently find and discard large parts of…
Extremely large-scale multiple-input multiple-output (XL-MIMO) is a key enabler for sixth-generation (6G) communications. However, near-field channel estimation is particularly challenging due to spherical-wave propagation and spatial…
We study nonlinear approximation in $\operatorname{BMO}$ from splines generated by a hierarchy of B-splines over regular multilevel nested partitions of $\mathbb R$. Companion Jackson and Bernstein estimates are established that allow to…
Wavelet families arise by scaling and translations of a prototype function, called the {\em {mother wavelet}}. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis…
Sparse representations using overcomplete dictionaries have proved to be a powerful tool in many signal processing applications such as denoising, super-resolution, inpainting, compression or classification. The sparsity of the…
Spline functions have long been used in numerical solution of differential equations. Recently it revives as isogeometric analysis, which offers integration of finite element analysis and NURBS based CAD into a single unified process.…
In sparse recovery, the unique sparsest solution to an under-determined system of linear equations is of main interest. This scheme is commonly proposed to be applied to signal acquisition. In most cases, the signals are not sparse…