2024/05/14 by Franz Luef, Luef, Franz, Johannes Testorf +3
Computer Science · Engineering · #Optical measurement and interference techniques #Image and Signal Denoising Methods #Photoacoustic and Ultrasonic Imaging
paper · pdf · doi:10.48550/arxiv.2405.08415
We give a criterion for higher-dimensional Gaussian Gabor frames, which is a reformulation of one of the main results in in a previous article by the first and last authors in more explicit terms. We use this formulation in order to extend a result of Romero, Ulanovskii, and Zlotnikov to lattices given by irrational rotations. We also show that this density criterion for Gaussian Gabor frames is generic in a certain sense. In addition, we also extend the methods of the first and last named authors to the pseudoeffective threshold which gives a condition for uniqueness in the Bargmann-Fock space. We also use this viewpoint to study super and multi-window Gabor frames with Hermitian windows. In particular, we find a density criterion for transcendental lattices.