相关论文: Sampling theorems on bounded domain
The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…
In this paper, we discuss to the nonuniform sampling problem in principal shift-invariant subspaces of mixed Lebesgue spaces. We proposed a fast reconstruction algorithm which allows to exactly reconstruct the functions in the principal…
We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its…
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…
A key problem in approximation theory is the recovery of high-dimensional functions from samples. In many cases, the functions of interest exhibit anisotropic smoothness, and, in many practical settings, the nature of this anisotropy may be…
We present new methods for solving a broad class of bound-constrained nonsmooth composite minimization problems. These methods are specially designed for objectives that are some known mapping of outputs from a computationally expensive…
In this work, we introduce new families of nonconforming approximation methods for reconstructing functions on general polygonal meshes. These methods are defined using degrees of freedom based on weighted moments of orthogonal polynomials…
This paper presents a supervised learning method to generate continuous cost-to-go functions of non-holonomic systems directly from the workspace description. Supervision from informative examples reduces training time and improves network…
We give a short survey of recent results on sparse-grid linear algorithms of approximate recovery and integration of functions possessing a unweighted or weighted Sobolev mixed smoothness based on their sampled values at a certain finite…
The Marchenko method retrieves the responses to virtual sources in the subsurface, accounting for all orders of multiples. The method is based on two integral representations for focusing and Green's functions. In discretized form these…
We consider the problem of reconstructing an unknown function $u\in L^2(D,\mu)$ from its evaluations at given sampling points $x^1,\dots,x^m\in D$, where $D\subset \mathbb R^d$ is a general domain and $\mu$ a probability measure. The…
We consider the problem of reconstructing missing data on a smooth manifold from incomplete and nonuniform samples. While classical methods for manifold approximation typically assume quasi-uniform data, their performance deteriorates…
We study the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. Our main interest is to obtain preasymptotic estimates for the corresponding sampling numbers. We obtain results in terms of the…
Magnetic resonance imaging (MRI) acquisition, reconstruction, and segmentation are usually processed independently in the conventional practice of MRI workflow. It is easy to notice that there are significant relevances among these tasks…
The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…
Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology. Since prevalent…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
We propose a manifold sampling algorithm for minimizing a nonsmooth composition $f= h\circ F$, where we assume $h$ is nonsmooth and may be inexpensively computed in closed form and $F$ is smooth but its Jacobian may not be available. We…