Related papers: Data Interpolation: An Efficient Sampling Alternat…
A simple model system is introduced for demonstrating how a single photon source might be used to transduce classical analog information. The theoretical scheme results in measurements of analog source samples that are (i) quantized in the…
Reducing noise caused by the instrumentation in observational data is a crucial step in data post-processing. A method is searched for that conserves most of the instrumental resolution and introduces as few methodical artefacts as…
Image interpolation is a special case of image super-resolution, where the low-resolution image is directly down-sampled from its high-resolution counterpart without blurring and noise. Therefore, assumptions adopted in super-resolution…
One way to investigate the precision of estimates likely to result from planned experiments and planned epidemiological studies is to simulate a large number of possible outcomes and analyse the sets of possible results. This appears to be…
We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific…
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…
Mixup and its variants form a popular class of data augmentation techniques.Using a random sample pair, it generates a new sample by linear interpolation of the inputs and labels. However, generating only one single interpolation may limit…
Consider a sparse multivariate polynomial f with integer coefficients. Assume that f is represented as a "modular black box polynomial", e.g. via an algorithm to evaluate f at arbitrary integer points, modulo arbitrary positive integers.…
This paper introduces a generalization of the empirical interpolation method (EIM) and the reduced basis method (RBM) in order to allow their combination with data mining and data assimilation. The purpose is to be able to derive sound…
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…
As urbanization proceeds at an astonishing rate, cities have to continuously improve their solutions that affect the safety, health and overall wellbeing of their residents. Smart city projects worldwide build on advanced sensor,…
The present paper proposes a data-driven sensor selection method for a high-dimensional nondynamical system with strongly correlated measurement noise. The proposed method is based on proximal optimization and determines sensor locations by…
We develop a formal framework for the behavioral comparison of linear systems across different time domains. We accomplish this by introducing the notion of system interpolation, which determines whether the input-state trajectories of a…
Approximation theorem is one of the most important aspects of numerical analysis that has evolved over the years with many different approaches. Some of the most popular approximation methods include the Lebesgue approximation theorem, the…
We obtain sampling and interpolation theorems in radial weighted spaces of analytic functions for weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted…
Sensor data has been playing an important role in machine learning tasks, complementary to the human-annotated data that is usually rather costly. However, due to systematic or accidental mis-operations, sensor data comes very often with a…
A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the…
In Helio- and asteroseismology, it is important to have continuous, uninterrupted, data sets. However, seismic observations usually contain gaps and we need to take them into account. In particular, if the gaps are not randomly distributed,…
Deep networks often exhibit a preference for "simple" solutions, and such a simplicity bias is widely believed to play a key role in generalization. Yet a broadly applicable, quantitative measure of simplicity remains elusive. We introduce…
Conventional sampling and interpolation commonly rely on discrete measurements. In this paper, we develop a theoretical framework for extrapolation of signals in higher dimensions from knowledge of the continuous waveform on bounded…