Related papers: Estimation of noisy cubic spline using a natural b…
Noise is a significant part within a millimeter-wave molecular line datacube. Analyzing the noise improves our understanding of noise characteristics, and further contributes to scientific discoveries. We measure the noise level of a single…
Despite the growing demand for accurate surface normal estimation models, existing methods use general-purpose dense prediction models, adopting the same inductive biases as other tasks. In this paper, we discuss the inductive biases needed…
We investigate a novel non-parametric regression-based clustering algorithm for longitudinal data analysis. Combining natural cubic splines with Gaussian mixture models (GMM), the algorithm can produce smooth cluster means that describe the…
We solve the problem of computing characteristic numbers of rational space curves with a cusp, where there may or may not be a condition on the node. The solution is given in the form of effective recursions. We give explicit formulas when…
We present a novel method for reliably explaining the predictions of neural networks. We consider an explanation reliable if it identifies input features relevant to the model output by considering the input and the neighboring data points.…
Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objective is the reconstruction of analysis-suitable models from…
Generalizing tensor-product splines to smooth functions whose control nets outline topological polyhedra, bi-cubic polyhedral splines form a piecewise polynomial, first-order differentiable space that associates one function with each…
Penalized spline smoothing is a popular and flexible method of obtaining estimates in nonparametric regression but the classical least-squares criterion is highly susceptible to model deviations and atypical observations. Penalized spline…
This paper proposes an image interpolation algorithm exploiting sparse representation for natural images. It involves three main steps: (a) obtaining an initial estimate of the high resolution image using linear methods like FIR filtering,…
In this paper we provide a priori error estimates with explicit constants for both the $L^2$-projection and the Ritz projection onto spline spaces of arbitrary smoothness defined on arbitrary grids. This extends the results recently…
Continuous representations are fundamental for modeling sampled data and performing computations and numerical simulations directly on the model or its elements. To effectively and efficiently address the approximation of point clouds we…
We study the singular stochastic wave equation on $\mathbb T^2$, with a cubic nonlinearity and Gaussian rough Mat\'ern forcing (a Fourier multiplier of order $\alpha>0$ applied to space-time white noise) and establish local well-posedness…
Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…
This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational…
We consider the problem of estimating an unknown coordinate-wise monotone function given noisy measurements, known as the isotonic regression problem. Often, only a small subset of the features affects the output. This motivates the sparse…
The P-splines of Eilers and Marx (1996) combine a B-spline basis with a discrete quadratic penalty on the basis coefficients, to produce a reduced rank spline like smoother. P-splines have three properties that make them very popular as…
This paper proposes a method for estimating a surface that contains a given set of points from noisy measurements. More precisely, by assuming that the surface is described by the zero set of a function in the span of a given set of…
Recently, a new signal analysis method based on a semi-classical approach has been proposed [1]. The main idea in this method is to interpret a signal as a potential of a Schrodinger operator and then to use the discrete spectrum of this…
Qubit noise spectroscopy is an important tool for the experimental investigation of open quantum systems. However, conventional techniques for noise spectroscopy are time-consuming, because they require measurements of the noise spectral…
We give an explicit formula for the expectation of the number of real lines on a random invariant cubic surface, i.e. a surface $Z\subset \mathbb{R}P^3$ defined by a random gaussian polynomial whose probability distribution is invariant…