The numerical application of the statistical reduced isometry property (StRIP) and statistical null space property (SNSP) is presented and demonstrated for the design of underwater acoustic line arrays. This recent approach predicts the theoretical utility of specific subsampled arrays for compressive sensing. Three subsamplings are presented: Random, Golomb, and Wichmann. The Golomb array has no repeated spacings. The Wichmann array includes every possible interval of spacings. The SNSP is shown insensitive to the cases presented. The StRIP of the Golomb array predicts superior invertibility and is shown to perform well using at-sea data.
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http://dx.doi.org/10.1121/1.4812817 | DOI Listing |
Med Biol Eng Comput
January 2025
Department of Electrical and Communication Engineering, United Arab Emirates University, Asharej, Al Ain, 15551, Abu Dhabi, United Arab Emirates.
Photoacoustic tomography (PAT) has emerged as a promising imaging modality for breast cancer detection, offering unique advantages in visualizing tissue composition without ionizing radiation. However, limited-view scenarios in clinical settings present significant challenges for image reconstruction quality and computational efficiency. This paper introduces novel unrolled deep learning networks based on split Bregman total variation (SBTV) and relaxed basis pursuit alternating direction method of multipliers (rBP-ADMM) algorithms to address these challenges.
View Article and Find Full Text PDFGeom Dedic
September 2024
Department of Mathematics, KU Leuven, Celestijnenlaan 200B - box 2400, 3001 Leuven, Belgium.
Coarse geometry studies metric spaces on the large scale. The recently introduced notion of coarse entropy is a tool to study dynamics from the coarse point of view. We prove that all isometries of a given metric space have the same coarse entropy and that this value is a coarse invariant.
View Article and Find Full Text PDFAnal Math Phys
May 2024
Department of Mathematics and Computer Science, University of Richmond, Richmond, VA 23173 USA.
If is a unitary operator on a separable complex Hilbert space , an application of the spectral theorem says there is a conjugation on (an antilinear, involutive, isometry on ) for which In this paper, we fix a unitary operator and describe of the conjugations which satisfy this property. As a consequence of our results, we show that a subspace is hyperinvariant for if and only if it is invariant for any conjugation for which .
View Article and Find Full Text PDFSci Rep
May 2024
Department of Computer Science, University of Liverpool, Liverpool, L69 3BX, UK.
Periodic material or crystal property prediction using machine learning has grown popular in recent years as it provides a computationally efficient replacement for classical simulation methods. A crucial first step for any of these algorithms is the representation used for a periodic crystal. While similar objects like molecules and proteins have a finite number of atoms and their representation can be built based upon a finite point cloud interpretation, periodic crystals are unbounded in size, making their representation more challenging.
View Article and Find Full Text PDFPhys Rev Lett
April 2024
Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain.
We show that some sets of quantum observables are unique up to an isometry and have a contextuality witness that attains the same value for any initial state. We prove that these two properties make it possible to certify any of these sets by looking at the statistics of experiments with sequential measurements and using any initial state of full rank, including thermal and maximally mixed states. We prove that this "certification with any full-rank state" (CFR) is possible for any quantum system of finite dimension d≥3 and is robust and experimentally useful in dimensions 3 and 4.
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