Related papers: Randomized Wavelets on Arbitrary Domains and Appli…
The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified. This is accomplished through detailed investigation of the…
We propose a novel deep learning framework for fast prediction of boundaries of two-dimensional simply connected domains using wavelets and Multi Resolution Analysis (MRA). The boundaries are modelled as (piecewise) smooth closed curves…
Masked Image Modeling (MIM) has garnered significant attention in self-supervised learning, thanks to its impressive capacity to learn scalable visual representations tailored for downstream tasks. However, images inherently contain…
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
Parallel MRI is a fast imaging technique that enables the acquisition of highly resolved images in space. It relies on $k$-space undersampling and multiple receiver coils with complementary sensitivity profiles in order to reconstruct a…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
In this study, we perform some analysis for the probability distributions in the space of frequency and time variables. However, in the domain of high frequencies, it behaves in such a way as the highly non-linear dynamics. The wavelet…
Limited-angle computed tomography (CT) is often used in clinical applications such as C-arm CT for interventional imaging. However, CT images from limited angles suffers from heavy artifacts due to incomplete projection data. Existing…
In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…
The emergence of large foundation models has propelled significant advances in various domains. The Segment Anything Model (SAM), a leading model for image segmentation, exemplifies these advances, outperforming traditional methods.…
We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random…
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…
A novel method for learning optimal, orthonormal wavelet bases for representing 1- and 2D signals, based on parallels between the wavelet transform and fully connected artificial neural networks, is described. The structural similarities…
Samplets are data adapted multiresolution analyses of localized discrete signed measures. They can be constructed on scattered data sites in arbitrary dimension such that they exhibit vanishing moments with respect to any prescribed set of…
For describing the probability distribution of the positions and times of particles performing anomalous motion, fractional PDEs are derived from the continuous time random walk models with waiting time distribution having divergent first…
Bayesian image restoration has had a long history of successful application but one of the limitations that has prevented more widespread use is that the methods are generally computationally intensive. The authors recently addressed this…
Due to their adaptive nature, empirical wavelets had several successes in many fields from engineering, science, medical signal/image processing. Recently, a general theoretical framework has been developed in the one-dimensional case,…
Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…