Related papers: Optimized Spline Interpolation
Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
We present Neural Splines, a technique for 3D surface reconstruction that is based on random feature kernels arising from infinitely-wide shallow ReLU networks. Our method achieves state-of-the-art results, outperforming recent neural…
In this paper, we formally investigate two mathematical aspects of Hermite splines which translate to features that are relevant to their practical applications. We first demonstrate that Hermite splines are maximally localized in the sense…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
Deep learning based methods have recently pushed the state-of-the-art on the problem of Single Image Super-Resolution (SISR). In this work, we revisit the more traditional interpolation-based methods, that were popular before, now with the…
This paper investigates a variational model for splines in the image metamorphosis model for the smooth interpolation of key frames in the space of images. The Riemannian manifold of images based on the metamorphosis model defines shortest…
Explicit pointwise error bounds for the interpolation of a smooth function by piecewise exponential splines of order four are given. Estimates known for cubic splines are extended to a natural class of piecewise exponential splines which…
We study the impedance spectra of woodwind instruments with arbitrary axisymmetric geometry. We perform piecewise interpolations of the instruments' profile, using interpolating functions amenable to analytic solutions of the Webster…
In this paper the approximation of the optimal compressor function using the first-degree spline functions and quadratic spline functions is done. Coefficients on which we form approximative spline functions are determined by solving…
We provide new general kernel selection rules thanks to penalized least-squares criteria. We derive optimal oracle inequalities using adequate concentration tools. We also investigate the problem of minimal penalty as described in [BM07].
The marriage of recurrent neural networks and neural ordinary differential networks (ODE-RNN) is effective in modeling irregularly-observed sequences. While ODE produces the smooth hidden states between observation intervals, the RNN will…
Topology optimization is one of the engineering tools for finding efficient design. For the material interpolation scheme, it is usual to employ the SIMP (Solid Isotropic Material with Penalization) or the homogenization based interpolation…
We consider channels affected by intersymbol interference with reduced-complexity, mutual information optimized, channel-shortening detection. For such settings, we optimize the transmit filter, taking into consideration the reduced…
Compactly supported shearlets have been studied in both theory and applications. In this paper, we construct symmetric compactly supported shearlet systems based on pseudo splines of type II. Specially, using B-splines, we construct…
In this work, we study the Hermite interpolation on $n$-dimensional non-equally spaced, rectilinear grids over a field $\Bbbk $ of characteristic zero, given the values of the function at each point of the grid and the partial derivatives…
We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…
This paper gives a general interpretation of Linear Prediction (LP) by interpolation framework different from the perspective of statistics. This interpretation is proved to be useful by several following results, such as: The mechanism of…
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…
We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to…