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Neuromorphic sampling is a paradigm shift in analog-to-digital conversion where the acquisition strategy is opportunistic and measurements are recorded only when there is a significant change in the signal. Neuromorphic sampling has given…

Signal Processing · Electrical Eng. & Systems 2023-06-09 Abijith Jagannath Kamath , Chandra Sekhar Seelamantula

We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as $ \hat g(\xi)= \prod_{j=1}^n (1+2\pi i\delta_j\xi)^{-1}…

Functional Analysis · Mathematics 2018-04-11 Karlheinz Gröchenig , José Luis Romero , Joachim Stöckler

Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…

Information Theory · Computer Science 2016-03-07 Yang Chen , Cheng Cheng , Qiyu Sun , Haichao Wang

The multiresolution analysis (MRA) associated with the Special affine Fourier transform (SAFT) provides a structured approach for generating orthonormal bases in \( L^2(\mathbb R) \), making it a powerful tool for advanced signal analysis.…

Functional Analysis · Mathematics 2026-01-12 Vikash K. Sahu , Waseem Z. Lone , Amit K. Verma

In this paper, we present a novel affine-invariant feature based on SIFT, leveraging the regular appearance of man-made objects. The feature achieves full affine invariance without needing to simulate over affine parameter space. Low-rank…

Computer Vision and Pattern Recognition · Computer Science 2014-08-08 Chao Yang , Shengnan Caih , Jingdong Wang , Long Quan

We consider bounded operators $A$ acting iteratively on a finite set of vectors $\{f_i : i\in I\}$ in a Hilbert space $\mathcal H$ and address the problem of providing necessary and sufficient conditions for the collection of iterates…

Functional Analysis · Mathematics 2017-11-15 C. Cabrelli , U. Molter , V. Paternostro , F. Philipp

Let Y={f(i), Af(i),..., A^{li} f(i): i in Omega}, where A is a bounded operator on l^2(I). The problem under consideration is to find necessary and sufficient conditions on A, Omega, {l_i:i in Omega} in order to recover any f \in l^2(I)…

Classical Analysis and ODEs · Mathematics 2014-10-01 A. Aldroubi , C. Cabrelli , U. Molter , S. Tang

In this note, we solve the dynamical sampling problem for a class of shift-preserving operators $L:V\to V$ acting on a finitely generated shift-invariant space $V$. We find conditions on $L$ and a finite set of functions of $V$ so that the…

Functional Analysis · Mathematics 2020-11-30 A. Aguilera , C. Cabrelli , D. Carbajal , V. Paternostro

Affine transformation is one of the most common transformations in nature, which is an important issue in the field of computer vision and shape analysis. And affine transformations often occur in both shape and color space simultaneously,…

Computer Vision and Pattern Recognition · Computer Science 2019-11-20 You Hao , Hanlin Mo , Qi Li , He Zhang , Hua Li

Sampling in shift-invariant spaces is a realistic model for signals with smooth spectrum. In this paper, we consider phaseless sampling and reconstruction of real-valued signals in a shift-invariant space from their magnitude measurements…

Information Theory · Computer Science 2017-02-22 Cheng Cheng , Junzheng Jiang , Qiyu Sun

Sampling shift-invariant (SI) signals with a high dynamic range poses a notable challenge in the domain of analog-to-digital conversion (ADC). It is essential for the ADC's dynamic range to exceed that of the incoming analog signal to…

Signal Processing · Electrical Eng. & Systems 2024-06-18 Yhonatan Kvich , Yonina C. Eldar

In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…

Numerical Analysis · Mathematics 2020-06-24 Lutz Kämmerer , Felix Krahmer , Toni Volkmer

The graph Fourier transform (GFT) is a fundamental tool in graph signal processing and has recently been extended to the graph fractional Fourier transform (GFRFT). Existing sampling methods in the GFRFT domain are primarily designed to…

General Mathematics · Mathematics 2026-05-27 Yu Zhang , Jia-Yin Peng , Bing-Zhao Li

Phase retrieval from phaseless short-time Fourier transform (STFT) measurements is known to be inherently unstable when measurements are taken with respect to a single window. While an explicit inversion formula exists, it is useless in…

Functional Analysis · Mathematics 2025-06-19 Rima Alaifari , Yunan Yang

This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…

Functional Analysis · Mathematics 2024-02-15 Kumari Priyanka , A. Antony Selvan

We consider the sampling problem for two-sided small Fock spaces $\mathcal{F}^p_{\alpha}$, for the full range $0 < p \le \infty$. We establish a geometric description of shift-invariant sampling sequences, i.e., sequences $\Lambda$ such…

Functional Analysis · Mathematics 2025-11-27 Yurii Belov , Mikhail Mironov

The recovery of bandlimited signals with high dynamic range is a hot issue in sampling research. The unlimited sampling theory expands the recordable range of traditional analog-to-digital converters (ADCs) arbitrarily, and the signal is…

Signal Processing · Electrical Eng. & Systems 2023-02-20 Hui Zhao , Bing-Zhao Li

The Fast Fourier Transform (FFT) is a numerical operation that transforms a function into a form comprised of its constituent frequencies and is an integral part of scientific computation and data analysis. The objective of our work is to…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-02-04 Sudhanshu Kulkarni , Burlen Loring , E. Wes Bethel

To obtain the initial pressure from the collected data on a planar sensor arrangement in Photoacoustic tomography, there exists an exact analytic frequency domain reconstruction formula. An efficient realization of this formula needs to…

Numerical Analysis · Mathematics 2015-01-14 Julian Schmid , Thomas Glatz , Behrooz Zabihian , Mengyang Liu , Wolfgang Drexler , Otmar Scherzer

We study the problem of sampling with derivatives in shift-invariant spaces generated by totally-positive functions of Gaussian type or by the hyperbolic secant. We provide sharp conditions in terms of weighted Beurling densities. As a…

Classical Analysis and ODEs · Mathematics 2022-05-04 Karlheinz Gröchenig , José Luis Romero , Joachim Stöckler