Live briefing
Everything about Total variation
Measure of local oscillation behavior
In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure. For a real-valued continuous function f, defined on an interval [a, b] ⊂ R, its total variation on the interval of definition is a measure of the one-dimensional arclength of the curve with parametric equation x ↦ f(x), for x ∈ [a, b]. Functions whose total variation is finite are called functions of bounded variation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Total variationA 5-minute orientation
- Skim a recent paper: Mesh Total Generalized Variation for DenoisingInfluential work since 2022
- Pick up a classic book: TVD flux-difference split methods for high-speed thermochemical nonequilibrium flows with strong shocksThe most-reprinted book on the subject
- Read the landmark paper: Nonlinear total variation based noise removal algorithmsCited 13,282 times
- Go sideways: Geometrical opticsA closely related topic
- Go sideways: Kernel embedding of distributionsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Nonlinear total variation based noise removal algorithms
Total Generalized Variation
Total variation blind deconvolution
Total-Variation-Diminishing Time Discretizations
Iterative Methods for Total Variation Denoising
A Total Variation Model for Retinex
The Total Variation Flow in RN
On the Equivalence of Soft Wavelet Shrinkage, Total Variation Diffusion, Total Variation Regularization, and SIDEs
🆕 Influential since 2022
📚 Books worth reading
- 📕TVD flux-difference split methods for high-speed thermochemical nonequilibrium flows with strong shocksClinton P. T. Groth · 1993
- 📕Fully discrete high-order TVD schemes for a scalar hyperbolic conservation lawJian Shi · 1993
- 📕A new class of high accuracy TVD schemes for hyperbolic conservation lawsSukumar Raman Chakravarthy · 1985
- 📕Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinatesH. C. Yee · 1985
- 📕Application of a new class of high accuracy TVD schemes to the Navier-Stokes equationsSukumar Raman Chakravarthy · 1985
- 📕Numerical simulation by TVD schemes of complex shock reflections from airfoils at high angle of attackYoung J. Moon · 1987
- 📕TVD regions for the weighted average flux (WAF) method as applied to a model hyperbolic conservation lawE. F. Toro · 1989
- 📕Application of second-order-accurate total variation diminishing (TVD) schemes to the Euler equations in general geometriesH. C. Yee · 1983
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Geometrical optics Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction…
- Kernel embedding of distributions In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which…
- Volume form In mathematics, a volume form or top-dimensional form is a differential form of degree equal to the differentiable manifold dimension. Thus on a manifold…
- Ewald–Oseen extinction theorem In optics, the Ewald–Oseen extinction theorem, sometimes referred to as just the extinction theorem, is a theorem that underlies the common understanding…
- Conservative vector field In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that…
- Transportation theory (mathematics) In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources…
- X-ray magnetic circular dichroism X-ray magnetic circular dichroism (XMCD) is a difference spectrum of two X-ray absorption spectra (XAS) taken in a magnetic field, one taken with left…
- Adjoint equation An adjoint equation is a linear differential equation, usually derived from its primal equation using integration by parts. Gradient values with respect…