Related papers: Evolution Equations on Gabor Transforms and their …
Image inversion is a fundamental task in generative models, aiming to map images back to their latent representations to enable downstream applications such as editing, restoration, and style transfer. This paper provides a comprehensive…
The notion of translation (shift) is straightforward in classical signal processing, however, it is challenging on an irregular graph structure. In this work, we present an approach to characterize the translation operator in various signal…
Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a…
Deep networks are now ubiquitous in large-scale multi-center imaging studies. However, the direct aggregation of images across sites is contraindicated for downstream statistical and deep learning-based image analysis due to inconsistent…
We consider Hamiltonian deformations of Gabor systems, where the window evolves according to the action of a Schr\"odinger propagator and the phase-space nodes evolve according to the corresponding Hamiltonian flow. We prove the stability…
Shifted and modulated Gaussian functions play a vital role in the representation of signals. We extend the theory into a quaternionic setting, using two exponential kernels with two complex numbers. As a final result, we show that every…
Generative Adversarial Networks (GANs) have significantly advanced image synthesis through mapping randomly sampled latent codes to high-fidelity synthesized images. However, applying well-trained GANs to real image editing remains…
Gene expression programming is an evolutionary optimization algorithm with the potential to generate interpretable and easily implementable equations for regression problems. Despite knowledge gained from previous optimizations being…
In several geophysical applications, such as full waveform inversion and data modelling, we are facing the solution of inhomogeneous Helmholtz equation. The difficulties of solving the Helmholtz equa- tion are two fold. Firstly, in the case…
The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section,…
While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L_2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the…
We use the method of similar operators to study a mixed problem for a differential equation with an involution and an operator-valued potential function. The differential operator defined by the equation is transformed into a similar…
The paper deals with the necessary and sufficient conditions for obtaining reconstruction formulae and sampling theorems for every function belonging to the principal shift invariant subspace of $L^2(\mathbb{H}^n)$, both in the time domain…
In these lecture notes, the representation theory of the Heisenberg group as well as Howe's construction of the metaplectic group by means of twisted convolution operators with generalized, complex Gaussians are reviewed, and it is shown…
Most textbooks introduce the concept of spin by presenting the Stern-Gerlach experiment with the aid of Newtonian atomic trajectories. However, to understand how both spatial and spin degrees of freedom evolve over time and how the latter…
Many geometric learning problems require invariants on heterogeneous product spaces, i.e., products of distinct spaces carrying different group actions, where standard techniques do not directly apply. We show that, when a group $G$ acts…
A promising approach to preserving model performance in linearized transformers is to employ position-based re-weighting functions. However, state-of-the-art re-weighting functions rely heavily on target sequence lengths, making it…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
In this article we are going to discuss the conjecture of Strohmer and Beaver for Gaussian Gabor systems. It asks for an optimal sampling pattern in the time-frequency plane, where optimality is measured in terms of the condition number of…
Steerable properties dominate the design of traditional filters, e.g., Gabor filters, and endow features the capability of dealing with spatial transformations. However, such excellent properties have not been well explored in the popular…