相关论文: On a new multivariate sampling paradigm and a poly…
B-splines $B_{q}$, $\Sc q > 1$, of quaternionic order $q$, for short quaternionic B-splines, are quaternion-valued piecewise M\"{u}ntz polynomials whose scalar parts interpolate the classical Schoenberg splines $B_{n}$, $n\in\N$, with…
The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem with fast decreasing coefficient, as well as a new modification of the corresponding interpolation formula applicable for general type non-vanishing bounded…
A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…
This article pertains to interpolation of Sobolev functions at shrinking lattices $h\mathbb{Z}^d$ from $L_p$ shift-invariant spaces associated with cardinal functions related to general multiquadrics,…
Sampling theory has benefited from a surge of research in recent years, due in part to the intense research in wavelet theory and the connections made between the two fields. In this survey we present several extensions of the Shannon…
In this work, we draw connections between the classical Shannon interpolation of bandlimited deterministic signals and the literature on estimating continuous-time random processes from their samples (known in various communities under…
In this paper we extend the Shepard-Bernoulli operators introduced in [6] to the bivariate case. These new interpolation operators are realized by using local support basis functions introduced in [23] instead of classical Shepard basis…
In this paper, we present new regularized Shannon sampling formulas related to the special affine Fourier transform (SAFT). These sampling formulas use localized sampling with special compactly supported window functions, namely B-spline,…
This report mainly focused on the basic concepts and the recovery methods for the random sampling. The recovery methods involve the orthogonal matching pursuit algorithm and the gradient-based total variation strategy. In particular, a fast…
In this paper, we discuss some numerical realizations of Shannon's sampling theorem. First we show the poor convergence of classical Shannon sampling sums by presenting sharp upper and lower bounds of the norm of the Shannon sampling…
In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…
Duchon's method of thin plate splines defines a polyharmonic interpolant to scattered data values as the minimizer of a certain integral functional. For transfinite interpolation, i.e. interpolation of continuous data prescribed on curves…
A new method for directly sampling the neutron resonance upscattering effect is presented. Alternatives have relied on inefficient rejection sampling techniques or large tabular storage of relative velocities. None of these approaches,…
The main result in this paper is an error estimate for interpolation biharmonic polysplines in an annulus $A\left( r_{1},r_{N}\right) $, with respect to a partition by concentric annular domains $A\left( r_{1} ,r_{2}\right) ,$ ....,…
We consider the reconstruction of a bandlimited function from its finite localized sample data. Truncating the classical Shannon sampling series results in an unsatisfactory convergence rate due to the slow decayness of the sinc function.…
The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from…
Assume that samples of a filtered version of a function in a shift-invariant space are avalaible. This work deals with the existence of a sampling formula involving these samples and having reconstruction functions with compact support.…
For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…
The fast reconstruction of a bandlimited function from its sample data is an essential problem in signal processing. In this paper, we consider the widely used Gaussian regularized Shannon sampling formula in comparison to regularized…