Related papers: Coupled Splines for Sparse Curve Fitting

This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…

In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…

We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems,…

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…

Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…

Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…

A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…

Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By…

We propose a novel B-spline trajectory optimization method for autonomous racing. We consider the unavailability of sophisticated race car and race track dynamics in early-stage autonomous motorsports development and derive methods that…

In this paper we introduce the class of infinite infimal convolution functionals and apply these functionals to the regularization of ill-posed inverse problems. The proposed regularization involves an infimal convolution of a continuously…

Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive…

This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…

We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…

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.…

Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…

We present a unified framework for 3D geometric abstraction using a single continuous 4D wire, parameterized as a B-spline with spatial coordinates and variable width $(x,y,z,w)$. Existing approaches typically represent shapes as…

Proximal gradient methods are popular in sparse optimization as they are straightforward to implement. Nevertheless, they achieve biased solutions, requiring many iterations to converge. This work addresses these issues through a suitable…

A univariate continuous function can always be decomposed as the sum of a non-increasing function and a non-decreasing one. Based on this property, we propose a non-parametric regression method that combines two spline-fitted monotone…

Spline functions are smooth piecewise polynomials widely used for interpolation and smoothing, and nonnegative spline smoothing is also studied for nonnegative data. Previous research used sufficient conditions for the nonnegativity of…

Our main interest in this paper is to study some approximation problems for classes of functions with mixed smoothness. We use technique, based on a combination of results from hyperbolic cross approximation, which were obtained in 1980s --…