Related papers: Phase retrieval from short-time Fourier transform …
Continuous symmetries are fundamental to many scientific and learning problems, yet they are often unknown a priori. Existing symmetry discovery approaches typically search directly in the space of transformation generators or rely on…
The number of phase wraps in 2D wrapped phase map can be completely eliminated, or greatly reduced by frequency shifting. But the wraps usually cannot be optimally reduced using the conventional fast Fourier transform (FFT) because the…
Factorial moments are convenient tools in particle physics to characterize the multiplicity distributions when phase-space resolution ($\Delta$) becomes small. They include all correlations within the system of particles and represent…
We consider the phase retrieval problem in which one tries to reconstruct a function from the modulus of its wavelet transform. We study the unicity and stability of the reconstruction. In the case where the wavelets are Cauchy wavelets, we…
In this work we develop an algorithm for signal reconstruction from the magnitude of its Fourier transform in a situation where some (non-zero) parts of the sought signal are known. Although our method does not assume that the known part…
These notes briefly discuss basic notions concerning locally compact abelian topological groups and Fourier transforms of functions on them.
Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose…
Algorithms for processing data in short-time batches are critical for both online and offline processing of streamed and large data respectively due to the quadratic relation between signal length and computational cost of convolution-based…
We study nonlinear determination problems in Hilbert spaces in which inner products are observed up to prescribed rotations in the complex plane. Given a Hilbert space $H$ and a subset $\Theta$ of the unit circle $\mathbb{T}$, we say that a…
We study phase retrieval for group frames arising from permutation representations, focusing on the action of the affine group of a finite field. We investigate various versions of the phase retrieval problem, including conjugate phase…
We obtain a characterisation of the Fourier transform on the space of Schwartz-Bruhat functions on locally compact Abelian groups. The result states that any appropriately additive bijection of the Schwartz space onto itself, which…
By using a coset of closed subgroup, we define a Fourier like transform for locally compact abelian (LCA) topological groups. We studied two wavelet multipliers and Landau-Pollak-Slepian operators on locally compact abelian topological…
We study the regularity of smooth functions whose derivatives are dominated by sequences of the form $M_p^{\tau,\s}=p^{\tau p^{\s}}$, $\tau>0$, $\s\geq1$. We show that such functions can be characterized through the decay properties of…
Phase retrieval problems in antenna measurements arise when a reference phase cannot be provided to all measurement locations. Phase retrieval algorithms require sufficiently many independent measurement samples of the radiated fields to be…
We introduce and investigate using Hilbert modules the properties of the Fourier algebra A(G) for a locally compact groupoid G. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a…
The problem of phase retrieval is revisited and studied from a fresh perspective. In particular, we establish a connection between the phase retrieval problem and the sensor network localization problem, which allows us to utilize the vast…
Recovering a signal from its Fourier magnitude is referred to as phase retrieval, which occurs in different fields of engineering and applied physics. This paper gives a new characterization of the phase retrieval problem. Particularly…
We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This…
Phase retrieval is the problem of reconstructing images from magnitude-only measurements. In many real-world applications the problem is underdetermined. When training data is available, generative models allow optimization in a…
The phase retrieval problem is a fundamental problem in many fields, which is appealing for investigation. It is to recover the signal vector $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots,…