相关论文: Enforcing uniqueness in one-dimensional phase retr…
Pulse Doppler radars suffer from range-Doppler ambiguity that translates into a trade-off between maximal unambiguous range and velocity. Several techniques, like the multiple PRFs (MPRF) method, have been proposed to mitigate this problem.…
This paper reports an effort to consolidate numerous coherence-based sparse signal recovery results available in the literature. We present a single theory that applies to general Hilbert spaces with the sparsity of a signal defined as the…
Gabor phase retrieval is the problem of reconstructing a signal from only the magnitudes of its Gabor transform. Previous findings suggest a possible link between unique solvability of the discrete problem (recovery from measurements on a…
We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature…
In one-dimensional case the search for presence of the anomalous phenomena in multiplicity distributions is usually performed in frame of the horizontal, vertical and mixed types of the analysis. We show that if the data involve a…
Phase retrieval refers to the problem of reconstructing an unknown vector $x_0 \in \mathbb{C}^n$ or $x_0 \in \mathbb{R}^n $ from $m$ measurements of the form $y_i = \big\vert \langle \xi^{\left(i\right)}, x_0 \rangle \big\vert^2 $, where $…
A conjecture is proposed concerning the recovery of a discrete magnitude spectrum through a nonlinear transformation involving the Newman's phase sequence. Given a discrete magnitude spectrum sampled from a continuous function, consider the…
While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize…
This work addresses fundamental issues related to the structure and conditioning of linear time-delayed models of non-linear dynamics on an attractor. While this approach has been well-studied in the asymptotic sense (e.g. for infinite…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
A new method for phase recovery from a single two-beam interferogram is presented. Conventional approaches, relying on trigonometric inversion followed by phase unfolding and unwrapping, are hindered by discontinuities typically addressed…
In this work, we propose a novel consistency-preserving loss function for recovering the phase information in the context of phase reconstruction (PR) and speech enhancement (SE). Different from conventional techniques that directly…
This work is devoted to the study of discrete ambiguities. For parametrized potentials, they arise when the parameters are fitted to a finite number of phase-shifts. It generates phase equivalent potentials. Such equivalence was suggested…
We present a new method to locate the starting points in time of an arbitrary number of (damped) delayed signals. For a finite data sequence, the method permits to first locate the starting point of the component with the longest delay, and…
The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
In this paper, the uncertainty principle of discrete signals associated with Quaternion Fourier transform is investigated. It suggests how sparsity helps in the recovery of missing frequency.
In this paper, we consider the phase retrieval problem in which one aims to recover a signal from the magnitudes of affine measurements. Let $\{{\mathbf a}_j\}_{j=1}^m \subset {\mathbb H}^d$ and ${\mathbf b}=(b_1, \ldots,…
The problem of separation of an observed sum of chaotic signals into the individual components in the presence of noise on the path to the observer is considered. A noise threshold is found above which high-quality separation is impossible.…
In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…