Related papers: Sampling of surfaces and functions in high dimensi…
Modern data sets, such as those in healthcare and e-commerce, are often derived from many individuals or systems but have insufficient data from each source alone to separately estimate individual, often high-dimensional, model parameters.…
Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the…
In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames.…
Sampling of signals belonging to a low-dimensional subspace has well-documented merits for dimensionality reduction, limited memory storage, and online processing of streaming network data. When the subspace is known, these signals can be…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
Surface topography refers to the geometric micro-structure of a surface and defines its tactile characteristics (typically in the sub-millimeter range). High-resolution 3D scanning techniques developed recently enable the 3D reconstruction…
In this paper, we investigate frames for $L_2[-\pi,\pi]^d$ consisting of exponential functions in connection to oversampling and nonuniform sampling of bandlimited functions. We derive a multidimensional nonuniform oversampling formula for…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
Successive differences on a sequence of data help to discover some smoothness features of this data. This was one of the main reasons for rewriting the classical interpolation formula in terms of such data differences. The aim of this paper…
We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…
Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of…
The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis…
We tensorize the Faber spline system from [14] to prove sequence space isomorphisms for multivariate function spaces with higher mixed regularity. The respective basis coefficients are local linear combinations of discrete function values…
We can, and should, do statistical inference on simulation models by adjusting the parameters in the simulation so that the values of {\em randomly chosen} functions of the simulation output match the values of those same functions…
The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…
Sampling recovery on some function classes is studied in this paper. Typically, function classes are defined by imposing smoothness conditions. It was understood in nonlinear approximation that structural conditions in the form of control…
Generalized sampling consists in the recovery of a function $f$, from the samples of the responses of a collection of linear shift-invariant systems to the input $f$. The reconstructed function is typically a member of a finitely generated…
In applications ranging from communications to genetics, signals can be modeled as lying in a union of subspaces. Under this model, signal coefficients that lie in certain subspaces are active or inactive together. The potential subspaces…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
Historically, analysis for multiscale PDEs is largely unified while numerical schemes tend to be equation-specific. In this paper, we propose a unified framework for computing multiscale problems through random sampling. This is achieved by…