Related papers: Wavelets and continuous wavelet transform for auto…
We consider the application of the polyharmonic subdivision wavelets (of Daubechies type) to Image Processing, in particular to Astronomical Images. The results show an essential advantage over some standard multivariate wavelets and a…
The rise of machine learning in image processing has created a gap between trainable data-driven and classical model-driven approaches: While learning-based models often show superior performance, classical ones are often more transparent.…
Deep neural networks face numerous challenges in hyperspectral image classification, including high-dimensional data, sparse ground object distributions, and spectral redundancy, which often lead to classification overfitting and limited…
The GHM multi-level discrete wavelet transform is proposed as preprocessing for image super resolution with convolutional neural networks. Previous works perform analysis with the Haar wavelet only. In this work, 37 single-level wavelets…
The theory of orthonormal wavelet bases is a useful tool in multifractal analysis, as it provides a characterization of the different exponents of pointwise regularities (H{\"o}lder, p-exponent, lacunarity, oscillation, etc.). However, for…
We identify the result of the continuous wavelet transform with the difference of solutions of two hyperbolic partial differential equations, for which wavelet's shift and scale are considered as independent variables on 2D plane. The…
Transformers have achieved great success in natural language processing. Due to the powerful capability of self-attention mechanism in transformers, researchers develop the vision transformers for a variety of computer vision tasks, such as…
Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences. Of particular importance is the analysis of wavefront sets and the correct…
We present a Parseval tight wavelet frame for the representation and analysis of velocity vector fields of incompressible fluids. Our wavelets have closed form expressions in the frequency and spatial domains, are divergence free in the…
Variational Autoencoders (VAE) are probabilistic deep generative models underpinned by elegant theory, stable training processes, and meaningful manifold representations. However, they produce blurry images due to a lack of explicit…
Volumetric maps are widely used in robotics due to their desirable properties in applications such as path planning, exploration, and manipulation. Constant advances in mapping technologies are needed to keep up with the improvements in…
Texture classification is an important and challenging problem in many image processing applications. While convolutional neural networks (CNNs) achieved significant successes for image classification, texture classification remains a…
The suboptimal performance of wavelets with regard to the approximation of multivariate data gave rise to new representation systems, specifically designed for data with anisotropic features. Some prominent examples of these are given by…
We discuss the concept of a mesoscopic wavefunction, first in a general context, as the concept of wavefunction has evolved, and then in a more specific context of modeling. The paper concentrates on a simple, abstract one-dimensional…
Low-light images suffer from complex degradation, and existing enhancement methods often encode all degradation factors within a single latent space. This leads to highly entangled features and strong black-box characteristics, making the…
Image registration, or alignment of two or more images covering the same scenes or objects, is of great interest in many disciplines such as remote sensing, medical imaging, astronomy, and computer vision. In this paper, we introduce a new…
New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is…
Within the neurosciences, to observe variability across time in the dynamics of an underlying brain process is neither new nor unexpected. Wavelets are essential in analyzing brain signals because, even within a single trial, brain signals…
We extend Robertson's theorem to apply to frames generated by the action of a discrete, countable abelian unitary group. Within this setup we use Stone's theorem and the theory of spectral multiplicity to analyze wandering frame…
We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series…