Applied mathematics | Digital geometry
Discrete tomography focuses on the problem of reconstruction of binary images (or finite subsets of the integer lattice) from a small number of their projections. In general, tomography deals with the problem of determining shape and dimensional information of an object from a set of projections. From the mathematical point of view, the object corresponds to a function and the problem posed is to reconstruct this function from its integrals or sums over subsets of its domain. In general, the tomographic inversion problem may be continuous or discrete. In continuous tomography both thedomain and the range of the function are continuous and line integrals are used. In discrete tomography the domain of the function may be either discrete or continuous, and the range of the function is a finite set of real, usually nonnegative numbers. In continuous tomography when a large number of projections is available, accurate reconstructions can be made by many different algorithms.It is typical for discrete tomography that only a few projections (line sums) are used. In this case, conventional techniques all fail. A special case of discrete tomography deals with the problem of the reconstruction ofa binary image from a small number of projections. The name discrete tomography is due to Larry Shepp, who organized the first meeting devoted to this topic (DIMACS Mini-Symposium on Discrete Tomography, September 19, 1994, Rutgers University). (Wikipedia).
The Two-Dimensional Discrete Fourier Transform
The two-dimensional discrete Fourier transform (DFT) is the natural extension of the one-dimensional DFT and describes two-dimensional signals like images as a weighted sum of two dimensional sinusoids. Two-dimensional sinusoids have a horizontal frequency component and a vertical frequen
From playlist Fourier
Fourier Transforms: Discrete Fourier Transform, Part 3
Data Science for Biologists Fourier Transforms: Discrete Fourier Transform Part 3 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton
From playlist Fourier
Connecting discrete and continuous systems
To have an effect in the real world, discrete systems have to sample sample continuous signals to operate on them and reconstruct their outputs to continuous signals. This video explains this and the problems associated with the z transform
From playlist Discrete
The Discrete Fourier Transform
This video provides a basic introduction to the very widely used and important discrete Fourier transform (DFT). The DFT describes discrete-time signals as a weighted sum of complex sinusoid building blocks and is used in applications such as GPS, MP3, JPEG, and WiFi.
From playlist Fourier
This video explains what is taught in discrete mathematics.
From playlist Mathematical Statements (Discrete Math)
Introduction to Discrete and Continuous Functions
This video defines and provides examples of discrete and continuous functions.
From playlist Introduction to Functions: Function Basics
Albert Fannjiang - From Tomographic Phase Retrieval to Projection Tomography - IPAM at UCLA
Recorded 11 October 2022. Albert Fannjiang of the University of California, Davis, presents "From Tomographic Phase Retrieval to Projection Tomography" at IPAM's Diffractive Imaging with Phase Retrieval Workshop. Abstract: We analyze measurement schemes under which 3D unwrapped phase retri
From playlist 2022 Diffractive Imaging with Phase Retrieval - - Computational Microscopy
[Discrete Mathematics] Finite State Machines
We do a quick introduction to finite state machines, creating our own, understanding what they do, and abstracting the purpose of these machines. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtu
From playlist Discrete Math 1
Gabriele Steidl: Stochastic normalizing flows and the power of patches in inverse problems
CONFERENCE Recording during the thematic meeting : "Learning and Optimization in Luminy" the October 4, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on C
From playlist Probability and Statistics
Holographic Tomography | MIT 2.71 Optics, Spring 2009
Holographic Tomography Instructor: Aditya Bhakta, Danny Codd View the complete course: http://ocw.mit.edu/2-71S09 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 2.71 Optics, Spring 2009
Samuli Siltanen: Reconstruction methods for ill-posed inverse problems - Part 1
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 Partial Differential Equations
Neža Mramor (2/17/21): An application of discrete Morse theory to robot motion planning
Title: An application of discrete Morse theory to robot motion planning Abstract: We will shortly recollect the basics of discrete Morse theory and two of its variants, parametric and fiberwise discrete Morse theory. We will then describe how it can be used to construct a continuous motio
From playlist AATRN 2021
Recovering quantum gates from few average fidelities - R. Kueng - Workshop 1 - CEB T2 2018
Richard Kueng (California Institute of Technology) / 17.05.2018 Recovering quantum gates from few average fidelities Characterizing quantum processes is a key task for the development of quantum technologies, especially at the noisy intermediate scale of today’s devices. One method for
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
Demetri Psaltis - Machine Learning for 3D Optical Imaging - IPAM at UCLA
Recorded 13 October 2022. Demetri Psaltis of the École Polytechnique Fédérale de Lausanne (EPFL) presents "Machine Learning for 3D Optical Imaging" at IPAM's Diffractive Imaging with Phase Retrieval Workshop. Abstract: In optical diffraction tomography (ODT), the 3D shape of an object is r
From playlist 2022 Diffractive Imaging with Phase Retrieval - - Computational Microscopy
Notation and Basic Signal Properties
http://AllSignalProcessing.com for free e-book on frequency relationships and more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Signals as functions, discrete- and continuous-time signals, sampling, images, periodic signals, displayi
From playlist Introduction and Background
Manuel Guizar-Sicairos - Resonant ptychography, 3D magnetization and chemical characterization
Recorded 10 October 2022. Manuel Guizar-Sicairos of the Paul Scherrer Institute presents "Resonant ptychography, applications to 3D magnetization and chemical characterization" at IPAM's Diffractive Imaging with Phase Retrieval Workshop. Abstract: Ptychography is an imaging technique that
From playlist 2022 Diffractive Imaging with Phase Retrieval - - Computational Microscopy
Ulugbek Kamilov: Signal processing for nonlinear diffractive imaging
Abstract: Can modern signal processing be used to overcome the diffraction limit? The classical diffraction limit states that the resolution of a linear imaging system is fundamentally limited by one half of the wavelength of light. This implies that conventional light microscopes cannot d
From playlist Probability and Statistics
DDPS | Cheap and robust adaptive reduced order models for nonlinear inversion and design
Description: Nonlinear inverse problems and other PDE-constrained optimization problems, such as structural design under many load cases, require the repeated solution of many discretized large linear systems (or nonlinear systems). For Newton-type methods we also need solutions for the ad
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
Generalized Radon transforms in tomography
Advanced Instructional School on Theoretical and Numerical Aspects of Inverse Problems URL: https://www.icts.res.in/program/IP2014 Dates: Monday 16 Jun, 2014 - Saturday 28 Jun, 2014 Description In Inverse Problems the goal is to determine the properties of the interior of an object from
From playlist Advanced Instructional School on Theoretical and Numerical Aspects of Inverse Problems