Timeβfrequency analysis | Wavelets
Curvelets are a non-adaptive technique for multi-scale object representation. Being an extension of the wavelet concept, they are becoming popular in similar fields, namely in image processing and scientific computing. Wavelets generalize the Fourier transform by using a basis that represents both location and spatial frequency. For 2D or 3D signals, directional wavelet transforms go further, by using basis functions that are also localized in orientation. A curvelet transform differs from other directional wavelet transforms in that the degree of localisation in orientation varies with scale. In particular, fine-scale basis functions are long ridges; the shape of the basis functions at scale j is by so the fine-scale bases are skinny ridges with a precisely determined orientation. Curvelets are an appropriate basis for representing images (or other functions) which are smooth apart from singularities along smooth curves, where the curves have bounded curvature, i.e. where objects in the image have a minimum length scale. This property holds for cartoons, geometrical diagrams, and text. As one zooms in on such images, the edges they contain appear increasingly straight. Curvelets take advantage of this property, by defining the higher resolution curvelets to be more elongated than the lower resolution curvelets. However, natural images (photographs) do not have this property; they have detail at every scale. Therefore, for natural images, it is preferable to use some sort of directional wavelet transform whose wavelets have the same aspect ratio at every scale. When the image is of the right type, curvelets provide a representation that is considerably sparser than other wavelet transforms. This can be quantified by considering the best approximation of a geometrical test image that can be represented using only wavelets, and analysing the approximation error as a function of . For a Fourier transform, the squared error decreases only as . For a wide variety of wavelet transforms, including both directional and non-directional variants, the squared error decreases as . The extra assumption underlying the curvelet transform allows it to achieve . Efficient numerical algorithms exist for computing the curvelet transform of discrete data. The computational cost of a curvelet transform is approximately 10β20 times that of an FFT, and has the same dependence of for an image of size . (Wikipedia).
#Cycloid: A curve traced by a point on a circle rolling in a straight line. (A preview of this Sunday's video.)
From playlist Miscellaneous
Philipp Grohs: Wavelets, shearlets and geometric frames - Part 2
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Analysis and its Applications
Free ebook http://tinyurl.com/EngMathYT A basic introduction to the curl of a vector field - one of the basic operations of vector calculus. I show how to calculate the curl and discuss its relationship with rotation and circulation density. Many examples are presented.
From playlist Engineering Mathematics
Philipp Grohs: Somes perspectives of computational harmonic analysis in numerics
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist 30 years of wavelets
Deep learning for scientific computing: 2 stories on the gap between theory & practice - Ben Adcock
Deep learning is being increasingly used for challenging problems in scientific computing. Theoretically, such efforts are supported by a large and growing body of literature on existence of deep neural networks with favourable approximation properties. Yet, these results often say very li
From playlist Interpretability, safety, and security in AI
Lisbeth Fajstrup interviewed by Martin Raussen (September 29, 2021)
Lisbeth Fajstrup interviewed by Martin Raussen (September 29, 2021) For more on the interview series, along with the advertisement posters, please see https://sites.google.com/view/aatrn/interviews
From playlist AATRN Interviews
Ingrid Daubechies - 4/4 Time-Frequency Localization and Applications
Abstract: In this 250th anniversary year of the birth of Joseph Fourier, it behoves us to talk of frequency and spectral analysis! The lectures shall visit a number of different techniques that have been developed and applied in the last 30 years, to carry out what engineers and applied m
From playlist Hadamard Lectures 2018 - Ingrid DAUBECHIES - Time-Frequency Localization and Applications
Ingrid Daubechies - 1/4 Time-Frequency Localization and Applications
Abstract: In this 250th anniversary year of the birth of Joseph Fourier, it behoves us to talk of frequency and spectral analysis! The lectures shall visit a number of different techniques that have been developed and applied in the last 30 years, to carry out what engineers and applied m
From playlist Hadamard Lectures 2018 - Ingrid DAUBECHIES - Time-Frequency Localization and Applications
Free ebook http://tinyurl.com/EngMathYT How to integrate over 2 curves. This example discusses the additivity property of line integrals (sometimes called path integrals).
From playlist Engineering Mathematics
Ingrid Daubechies - 3/4 Time-Frequency Localization and Applications
Abstract: In this 250th anniversary year of the birth of Joseph Fourier, it behoves us to talk of frequency and spectral analysis! The lectures shall visit a number of different techniques that have been developed and applied in the last 30 years, to carry out what engineers and applied m
From playlist Hadamard Lectures 2018 - Ingrid DAUBECHIES - Time-Frequency Localization and Applications
From playlist Drawing a sphere
Ingrid Daubechies - 2/4 Time-Frequency Localization and Applications
Abstract: In this 250th anniversary year of the birth of Joseph Fourier, it behoves us to talk of frequency and spectral analysis! The lectures shall visit a number of different techniques that have been developed and applied in the last 30 years, to carry out what engineers and applied m
From playlist Hadamard Lectures 2018 - Ingrid DAUBECHIES - Time-Frequency Localization and Applications
(ML 7.7.A1) Dirichlet distribution
Definition of the Dirichlet distribution, what it looks like, intuition for what the parameters control, and some statistics: mean, mode, and variance.
From playlist Machine Learning
What are the x and y intercepts of a linear equation
π Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist β‘οΈGraph Linear Equations | Learn About
Quickstart for Desktop Version Example 1: Circumcircle of a Triangle
From playlist Quickstart for Desktop
Linear Equations from the Graph of the Line, No. 1
Shows how to write the equation of a line in the slope intercept from from the graph of the line. You can link to all my videos at my website: https://www.stepbystepscience.com
From playlist Algebra; Linear Equations
In this video I take a look at the slope of a curve (that is not straight line).
From playlist Biomathematics
Artificial Intelligence Full Course in 10 Hours [2023] | Artificial Intelligence Tutorial | Edureka
π₯ ππππ‘π’π§π ππππ«π§π’π§π ππ§π π’π§πππ« πππ¬πππ«π¬ ππ«π¨π π«ππ¦ : https://www.edureka.co/masters-program/machine-learning-engineer-training (Use Code "πππππππππ") This Edureka video on "Artificial Intelligence Full Course" will provide you with a comprehensive and detailed knowledge of Artificial Intelligence
From playlist Artificial Intelligence Tutorial For Beginners | Edureka
What is everything you need to know to graph an equation in slope intercept form
π Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist β‘οΈGraph Linear Equations | Learn About