Related papers: Simulation of Gegenbauer Processes using Wavelet P…
We analyse the Gaussian wave packet transform. Based on the Fourier inversion formula and a partition of unity, which is formed by a collection of Gaussian basis functions, a new representation of square-integrable functions is presented.…
We consider a random process $Y(t)=\exp\{X(t)\}$, where $X(t)$ is a centered second-order process which correlation function $R(t,s)$ can be represented as $\int_{\mathbb{R}} u(t,y)\overline{u(s,y)} dy.$ A multiplicative wavelet-based…
In this paper we present an algorithm for analog simulation of electronic circuits involving a spline Galerkin method with wavelet-based adaptive refinement. Numerical tests show that a first algorithm prototype, build within a productively…
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…
A non-decimated wavelet transform (NDWT) is a popular version of wavelet transforms because of its many advantages in applications. The inherent redundancy of this transform proved beneficial in tasks of signal denoising and scaling…
We describe the construction of a spherical wavelet analysis through the inverse stereographic projection of the Euclidean planar wavelet framework, introduced originally by Antoine and Vandergheynst and developed further by Wiaux et al.…
Transformers have revolutionized AI in natural language processing and computer vision, but their large computation and memory demands pose major challenges for hardware acceleration. In practice, end-to-end throughput is often limited by…
The characterization of particle diffusion is a classical problem in physics and probability theory. The field of microrheology is based on experiments in which microscopic tracer beads are placed into a non-Newtonian fluid and tracked…
Transformer-based architectures have advanced medical image analysis by effectively modeling long-range dependencies, yet they often struggle in 3D settings due to substantial memory overhead and insufficient capture of fine-grained local…
Wavelets have proven to be highly successful in several signal and image processing applications. Wavelet design has been an active field of research for over two decades, with the problem often being approached from an analytical…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
Factorization of compact wavelet matrices into primitive ones has been known for more than 20 years. This method makes it possible to generate wavelet matrix coefficients and also to specify them by their first row. Recently, a new…
We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on…
In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…
It was also shown recently that GUP predicts potentially measurable corrections to the `doubling time' of freely moving Gaussian atomic and molecular wavepackets with a favorable combination of three parameters, {\it e.g.} mass, initial…
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
This paper addresses the problem of finding a B-term wavelet representation of a given discrete function $f \in \real^n$ whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
In this paper, we derive a new class of methods for the classic 2D phase unwrapping problem of recovering a phase function from its wrapped form. For this, we consider the wrapped phase as a wavefront aberration in an optical system, and…