Related papers: Directional spin wavelets on the sphere
The deflection of ultra-high energy cosmic rays depends on the shape of the injection spectrum of the source and the pervasive cosmic magnetic fields. In this work it is applied the wavelet transform on the sphere to search for energy…
A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the…
We present a rotation-equivariant unsupervised learning framework for the sparse deconvolution of non-negative scalar fields defined on the unit sphere. Spherical signals with multiple peaks naturally arise in Diffusion MRI (dMRI), where…
Large data-sets defined on the sphere arise in many fields. In particular, recent and forthcoming observations of the anisotropies of the cosmic microwave background (CMB) made on the celestial sphere contain approximately three and fifty…
Objective detection of specific patterns in statistical distributions, like groupings or gaps or abrupt transitions between different subsets, is a task with a rich range of applications in astronomy: Milky Way stellar population analysis,…
Analyzing scalar and vector fields on the sphere, such as temperature or wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector…
We adress the problem of spherical deconvolution in a non parametric statistical framework, where both the signal and the operator kernel are subject to error measurements. After a preliminary treatment of the kernel, we apply a…
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…
The paper shows that under some mild conditions $n$-dimensional spherical wavelets derived from approximate identities build semi-continuous frames. Moreover, for sufficiently dense grids Poisson wavelets on $n$-dimensional spheres…
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…
We present a method for efficient spin wave guiding within the magnonic nanostructures. Our technique is based on the anomalous refraction in the metamaterial flat slab. The gradual change of the material parameters (saturation…
In this article, we investigate the application of wavelet packet transform as a novel spectrum sensing approach. The main attraction for wavelet packets is the tradeoffs they offer in terms of satisfying various performance metrics such as…
This paper presents a framework for time-causal wavelet analysis. It targets real-time processing of temporal signals, where data from the future are not available. The study builds upon temporal scale-space theory, originating from a…
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…
We theoretically study the scattering of spin waves from a sharp domain wall in an antiferromagnetic spin chain. While the continuum model for an antiferromagnetic material yields the well-known result that spin waves can pass through a…
We address the question of designing isotropic analysis functions on the sphere which are perfectly limited in the spectral domain and optimally localized in the spatial domain. This work is motivated by the need of localized analysis tools…
The continuous wavelet transform has become a widely used tool in applied science during the last decade. In this article we discuss some generalizations coming from actions of closed subgroups of $\mathrm{GL}(n,\mathbb{R})$ acting on…
Here we present a method of constructing steerable wavelet frames in $L_2(\mathbb{R}^d)$ that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the need…
Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…
Designing a convolution for a spherical neural network requires a delicate tradeoff between efficiency and rotation equivariance. DeepSphere, a method based on a graph representation of the sampled sphere, strikes a controllable balance…