Related papers: Effective support, Dirac combs, and signal recover…
The classical shift retrieval problem considers two signals in vector form that are related by a shift. The problem is of great importance in many applications and is typically solved by maximizing the cross-correlation between the two…
Suppose we are given a vector $f$ in $\R^N$. How many linear measurements do we need to make about $f$ to be able to recover $f$ to within precision $\epsilon$ in the Euclidean ($\ell_2$) metric? Or more exactly, suppose we are interested…
Letting $T$ denote an ergodic transformation of the unit interval and letting $f \colon [0,1)\to \mathbb{R}$ denote an observable, we construct the $f$-weighted return time measure $\mu_y$ for a reference point $y\in[0,1)$ as the weighted…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
In this paper we are interested in the inverse problem of recovering a compact supported function from its truncated Fourier transform. We derive new Lipschitz stability estimates for the inversion in terms of the truncation parameter. The…
We demonstrate that the Dirac representation theory can be effectively adjusted and applied to signal theory. The main emphasis is on orthogonality as the principal physical requirement. The particular role of the identity and projection…
In this paper, we show the possibility of recovering a sum of Dirac measures on the rotation group $SO(3)$ from its low degree moments with respect to Wigner D-functions only. The main Theorem of the paper states, that exact recovery from…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
Shannon's sampling theorem is one of the cornerstone topics that is well understood and explored, both mathematically and algorithmically. That said, practical realization of this theorem still suffers from a severe bottleneck due to the…
We study perturbed Dirac operators of the form $ D_s= D + s{\cal A} :\Gamma(E)\rightarrow \Gamma(F)$ over a compact Riemannian manifold $(X, g)$ with symbol $c$ and special bundle maps ${\cal A} : E\rightarrow F$ for $s>>0$. Under a simple…
Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…
We propose a new penalty, the springback penalty, for constructing models to recover an unknown signal from incomplete and inaccurate measurements. Mathematically, the springback penalty is a weakly convex function. It bears various…
In practice most functional data cannot be recorded on a continuum, but rather at discrete time points. It is also quite common that these measurements come with an additive error, which one would like eliminate for the statistical…
Integrated sensing and communication (ISAC) is increasingly expected to operate under aggressive spectrum reuse, where co-channel orthogonal frequency division multiplexing (OFDM) interference can be catastrophic for data recovery on the…
We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that perfect recovery is possible for graph signals bandlimited…
Topological signals are variables or features associated with both nodes and edges of a network. Recently, in the context of Topological Machine Learning, great attention has been devoted to signal processing of such topological signals.…
Suppose we wish to recover a signal x in C^n from m intensity measurements of the form |<x,z_i>|^2, i = 1, 2,..., m; that is, from data in which phase information is missing. We prove that if the vectors z_i are sampled independently and…
We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The law of large numbers and the central limit theorem suggest…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random…