Related papers: Reconstruction of Bandlimited Functions from Unsig…
Weighted average sampling is more practical and numerically more stable than sampling at single points as in the classical Shannon sampling framework. Using the frame theory, one can completely reconstruct a bandlimited function from its…
We consider the problem of random sampling for band-limited functions. When can a band-limited function $f$ be recovered from randomly chosen samples $f(x_j), j\in \mathbb{N}$? We estimate the probability that a sampling inequality of the…
Reconstructing a band-limited function from its finite sample data is a fundamental task in signal analysis. A Gaussian regularized Shannon sampling series has been proved to be able to achieve exponential convergence for uniform sampling.…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
In this paper we study the reconstruction of a bandlimited signal from samples generated by the integrate and fire model. This sampler allows us to trade complexity in the reconstruction algorithms for simple hardware implementations, and…
Instead of sampling a function at a single point, average sampling takes the weighted sum of function values around the point. Such a sampling strategy is more practical and more stable. In this note, we present an explicit method with an…
In this paper we consider the following problem of phase retrieval: Given a collection of real-valued band-limited functions $\{\psi_{\lambda}\}_{\lambda\in \Lambda}\subset L^2(\mathbb{R}^d)$ that constitutes a semi-discrete frame, we ask…
We analyze the problem of reconstruction of a bandlimited function $f$ from the space-time samples of its states $f_t=\phi_t\ast f$ resulting from the convolution with a kernel $\phi_t$. It is well-known that, in natural phenomena, uniform…
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…
We study the recovery of functions in real spline spaces from unsigned sampled values. We consider two types of recovery. The one is to recover functions locally from finitely many unsigned samples. And the other is to recover functions on…
Recently efforts have been made to use generalized sinc functions to perfectly reconstruct various kinds of non-bandlimited signals. As a consequence, perfect reconstruction sampling formulas have been established using such generalized…
We provide sufficient conditions on a family of functions $(\phi_\alpha)_{\alpha\in A}:\mathbb{R}^d\to\mathbb{R}$ for sampling of multivariate bandlimited functions at certain nonuniform sequences of points in $\mathbb{R}^d$. We consider…
We consider sampling strategies for a class of multivariate bandlimited functions $f$ that have a spectrum consisting of disjoint frequency bands. Taking advantage of the special spectral structure, we provide formulas relating $f$ to the…
An inverse nonequispaced fast Fourier transform (iNFFT) is a fast algorithm to compute the Fourier coefficients of a trigonometric polynomial from nonequispaced sampling data. However, various applications such as magnetic resonance imaging…
We study the reconstruction of bandlimited fields from samples taken at unknown but statistically distributed sampling locations. The setup is motivated by distributed sampling where precise knowledge of sensor locations can be difficult.…
Noise-shaping quantization techniques are widely used for converting bandlimited signals from the analog to the digital domain. They work by ``shaping" the quantization noise so that it falls close to the reconstruction operator's null…
The paper investigates possibility of recovery of sequences from their decimated subsequences. It is shown that this recoverability is associated with certain spectrum degeneracy of a new kind, and that a sequences of a general kind can be…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
In this paper, we address the problem of reconstructing multiband signals from modulo-folded, pointwise samples within the Unlimited Sensing Framework (USF). Focusing on a low-complexity, single-channel acquisition setup, we establish…
In this paper we consider the problem of approximating function evaluations $f(\boldsymbol x_j)$ at given nonequispaced points $\boldsymbol x_j$, $j=1,\dots N$, of a bandlimited function from given values $\hat{f}(\boldsymbol k)$,…