Everything about Diffusion wavelets
Diffusion wavelets are a fast multiscale framework for the analysis of functions on discrete structures like graphs, manifolds, and point clouds in Euclidean space. Diffusion wavelets are an extension of classical wavelet theory from harmonic analysis. Unlike classical wavelets whose basis functions are predetermined, diffusion wavelets are adapted to the geometry of a given diffusion operator. Moreover, the diffusion wavelet basis functions are constructed by dilation using the dyadic powers of. These dyadic powers of diffusion over the space and propagate local relationships in the function throughout the space until they become global. And if the rank of higher powers of decrease, then these higher powers become compressible. From these decaying dyadic powers of comes a chain of decreasing subspaces. These subspaces are the scaling function approximation subspaces, and the differences in the subspace chain are the wavelet subspaces. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Diffusion waveletsA 5-minute orientation
- Skim a recent paper: Low-Light Image Enhancement with Wavelet-Based Diffusion ModelsInfluential work since 2022
- Pick up a classic book: Harmonic AnalysisThe most-reprinted book on the subject
- Read the landmark paper: Diffusion waveletsCited 503 times
- Go sideways: Proto-value functionA closely related topic
- Go sideways: Automatic basis function constructionA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Diffusion wavelets
Wavelets method for the time fractional diffusion-wave equation
Application of p-Adic Wavelets to Model Reaction–Diffusion Dynamics in Random Porous Media
Numerical solution of the convection diffusion equations by the second kind Chebyshev wavelets
Special issue on diffusion maps and wavelets
Admissible Diffusion Wavelets and Their Applications in Space-Frequency Processing
Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method
Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions
🆕 Influential since 2022
Low-Light Image Enhancement with Wavelet-Based Diffusion Models
Gegenbauer wavelets collocation technique for the nonlinear Fisher’s reaction–diffusion equation with application arising in biological and chemical sciences
Wavelets computational modeling of nonlinear coupled reaction–diffusion models arising in chemical processes
A weighted social network publishing method based on diffusion wavelets transform and differential privacy
On the Inverse Problem of Time-Dependent Coefficient in a Time Fractional Diffusion Problem by Newly Defined Monic Laquerre Wavelets
đź“š Books worth reading
- 📕Harmonic AnalysisPalle E. T. Jorgensen · 2018
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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