Related papers: From cardinal spline wavelet bases to highly coher…
W. C. Lang determined wavelets on Cantor dyadic group by using Multiresolution analysis method. In this paper we have given characterization of wavelet sets on Cantor dyadic group providing another method for the construction of wavelets.…
It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters…
Large language model (LLM) architectures are often described as functionally hierarchical: Early layers process syntax, middle layers begin to parse semantics, and late layers integrate information. The present work revisits these ideas.…
Convolutional neural networks (CNNs) have shown great capability of solving various artificial intelligence tasks. However, the increasing model size has raised challenges in employing them in resource-limited applications. In this work, we…
Mesoscale structures can often be described as fractional dimensional across a wide range of scales. We consider a $\gamma$ dimensional measure embedded in an $N$ dimensional space and discuss how to determine its dimension, both in $N$…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider the applications of discrete wavelet analysis…
Both pixel-based scale saliency (PSS) and basis project methods focus on multiscale analysis of data content and structure. Their theoretical relations and practical combination are previously discussed. However, no models have ever been…
In this paper high resolution wave probe records are examined using wavelet techniques with a view to determining the sources and relative contributions of capillary wave energy along representative wind wave forms. Wavelets enable…
A wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a collection, or system, of unitary operators. We will describe the operator-interpolation approach to wavelet theory using the…
We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended…
This paper presents a structured dictionary-based model for hyperspectral data that incorporates both spectral and contextual characteristics of a spectral sample, with the goal of hyperspectral image classification. The idea is to…
Variational Autoencoders (VAEs) are powerful generative models capable of learning compact latent representations. However, conventional VAEs often generate relatively blurry images due to their assumption of an isotropic Gaussian latent…
Recently single image super resolution is very important research area to generate high resolution image from given low resolution image. Algorithms of single image resolution are mainly based on wavelet domain and spatial domain. Filters…
We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fast-oscillation function by the solution of the diffusion differential equations. The most important advantage of…
We introduce a framework for spline spaces of hierarchical type, based on a parent-children relation, which is very convenient for the analysis as well as the implementation of adaptive isogeometric methods. Such framework makes it simple…
The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable…
The rise of generative chat-based Large Language Models (LLMs) over the past two years has spurred a race to develop systems that promise near-human conversational and reasoning experiences. However, recent studies indicate that the…
A relativistic generalisation of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context. It is shown that there…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set. We study a cardinality constrained…