相关论文: On stable reconstructions from nonuniform Fourier …
This paper considers the recovery of continuous signals in infinite dimensional spaces from the magnitude of their frequency samples. It proposes a sampling scheme which involves a combination of oversampling and modulations with complex…
We consider the recovery of a continuous domain piecewise constant image from its non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities/edges of the image are localized to the zero levelset of…
This paper is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourier transform of a time-dependent source…
Using Coherent-State (CS) techniques, we prove a sampling theorem for holomorphic functions on the hyperboloid (or its stereographic projection onto the open unit disk $\mathbb D_1$), seen as a homogeneous space of the pseudo-unitary group…
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 $\hat{f}(\boldsymbol k)$,…
This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
This paper is concerned with function reconstruction from samples. The sampling points used in several approaches are (1) structured points connected with fast algorithms or (2) unstructured points coming from, e.g., an initial random draw…
We investigate the problem of reconstructing a 2D piecewise smooth function from its bandlimited Fourier measurements. This is a well known and well studied problem with many real world implications, in particular in medical imaging. While…
We study the problem of stable reconstruction of the short-time Fourier transform from samples taken from trajectories in $\R^2$. We first consider the interplay between relative density of the trajectory and the reconstruction property.…
In some applications, one is interested in reconstructing a function $f$ from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we…
This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization. In particular, we show that from O(slog(N)) nonadaptive linear measurements, an…
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.…
We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…
We analyze signal recovery when samples are taken concomitantly from a signal and its Fourier transform. This two-sided sampling framework extends classical one-sided reconstruction and is particularly useful when measurements in either…
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…
This paper studies several aspects of signal reconstruction of sampled data in spaces of bandlimited functions. In the first part, signal spaces are characterized in which the classical sampling series uniformly converge, and we investigate…
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…
We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models…
This paper considers the use of total variation regularization in the recovery of approximately gradient sparse signals from their noisy discrete Fourier samples in the context of compressed sensing. It has been observed over the last…