Related papers: Local and Global Phaseless Sampling in Real Spline…
This paper tackles the unconstrained minimization of a class of nonsmooth and nonconvex functions that can be written as finite max-functions. A gradient and function-based sampling method is proposed which, under special circumstances,…
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 studied linear weighted sampling algorithms and their optimality for approximate recovery of functions with mixed smoothness on $\mathbb{R}^d$ from a set of $n$ their sampled values. Functions to be recovered are in weighted Sobolev…
Mobile sensing has been recently proposed for sampling spatial fields, where mobile sensors record the field along various paths for reconstruction. Classical and contemporary sampling typically assumes that the sampling locations are…
Let $\xi = \{x^j\}_{j=1}^n$ be a grid of $n$ points in the $d$-cube ${\II}^d:=[0,1]^d$, and $\Phi = \{\phi_j\}_{j =1}^n$ a family of $n$ functions on ${\II}^d$. We define the linear sampling algorithm $L_n(\Phi,\xi,\cdot)$ for an…
We study optimal algorithms in adaptive sampling recovery of smooth functions defined on the unit $d$-cube ${\II}^d:= [0,1]^d$. The recovery error is measured in the quasi-norm $\|\cdot\|_q$ of $L_q := L_q(\II^d)$. For $B$ a subset in…
We obtain new sampling discretization results in Orlicz norms on finite dimensional spaces. As applications, we study sampling recovery problems, where the error of the recovery process is calculated with respect to different Orlicz norms.…
Given pointwise samples of an unknown function belonging to a certain model set, one seeks in Optimal Recovery to recover this function in a way that minimizes the worst-case error of the recovery procedure. While it is often known that…
We introduce a continuous domain framework for the recovery of points on a surface in high dimensional space, represented as the zero-level set of a bandlimited function. We show that the exponential maps of the points on the surface…
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…
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…
Spatial sampling is traditionally studied in a static setting where static sensors scattered around space take measurements of the spatial field at their locations. In this paper we study the emerging paradigm of sampling and reconstructing…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…
Several imaging algorithms including patch-based image denoising, image time series recovery, and convolutional neural networks can be thought of as methods that exploit the manifold structure of signals. While the empirical performance of…
We proved that the phaseless sampling (PLS) in the linear-phase modulated shift-invariant space (SIS) $V(e^{\textbf{i}\alpha \cdot}\varphi), \alpha\neq0,$ is impossible even though the real-valued function $\varphi$ enjoys the full spark…
In this paper, we develop and analyze a rigorous multiscale upscaling method for dual continuum model, which serves as a powerful tool in subsurface formation applications. Our proposed method is capable of identifying different continua…
The recovery of an unknown signal from its linear measurements is a fundamental problem spanning numerous scientific and engineering disciplines. Commonly, prior knowledge suggests that the underlying signal resides within a known algebraic…
In this paper, we introduce a computational framework for recovering a high-resolution approximation of an unknown function from its low-resolution indirect measurements as well as high-resolution training observations by merging the…
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…
The conjugate phase retrieval problem concerns the determination of a complex-valued function, up to a unimodular constant and conjugation, from its magnitude observations. It can also be considered as a conjugate phaseless sampling and…