Related papers: Coupled Splines for Sparse Curve Fitting
In many classification problems it is desirable to output well-calibrated probabilities on the different classes. We propose a robust, non-parametric method of calibrating probabilities called SplineCalib that utilizes smoothing splines to…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
Penalized spline regression is a popular method for scatterplot smoothing, but there has long been a debate on how to construct confidence intervals for penalized spline fits. Due to the penalty, the fitted smooth curve is a biased estimate…
While the common environment representation in structure from motion is given by a sparse point cloud, the community has also investigated the use of lines to better enforce the inherent regularities in man-made surroundings. Following the…
In this paper, we develop approximation error estimates as well as corresponding inverse inequalities for B-splines of maximum smoothness, where both the function to be approximated and the approximation error are measured in standard…
We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree…
BSplines are one of the most promising curves in computer graphics. They are blessed with some superior geometric properties which make them an ideal candidate for several applications in computer aided design industry. In this article,…
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
We present a simple yet powerful framework for solving inverse problems by leveraging automatic differentiation. Our method is broadly applicable whenever a smooth cost function can be defined near the true solution, and a numerical…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
A method is proposed to construct spiral curves by inversion of a spiral arc of parabola. The resulting curve is rational of 4-th order. Proper selection of the parabolic arc and parameters of inversion allows to match a wide range of…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial…
Iteratively reweighted least square (IRLS) is a popular approach to solve sparsity-enforcing regression problems in machine learning. State of the art approaches are more efficient but typically rely on specific coordinate pruning schemes.…
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…