Канал: Andrew Reader

Visual Training of a CNN as a Denoiser (Deep Image Prior)

Visual Training of a CNN as a Denoiser (Deep Image Prior)

Simple AI image processing (deep image prior)

Simple AI image processing (deep image prior)

Iterative Image Reconstruction

Iterative Image Reconstruction

Size of the Atomic Nucleus

Size of the Atomic Nucleus

Schrödinger's Cat: Quantum Superposition

Schrödinger's Cat: Quantum Superposition

PET sinograms & backprojection

PET sinograms & backprojection

Understand 2D k-space, Fourier Synthesis & MRI!

Understand 2D k-space, Fourier Synthesis & MRI!

Wave-particle duality, wave functions, quantum superposition, wave function collapse

Wave-particle duality, wave functions, quantum superposition, wave function collapse

Heisenberg's Uncertainty Principle, Momentum and Spatial Frequency

Heisenberg's Uncertainty Principle, Momentum and Spatial Frequency

Bohr’s Quantum Leap in Atomic Modelling with Stunning Agreement with Experimental Results!

Bohr’s Quantum Leap in Atomic Modelling with Stunning Agreement with Experimental Results!

Photoelectric Effect Explained with Equations: Einstein's Nobel Prize Winning Work on Photons

Photoelectric Effect Explained with Equations: Einstein's Nobel Prize Winning Work on Photons

Millikan's Nobel Prize: Oil Drop Experiment for Measuring the Fundamental Unit of Electric Charge

Millikan's Nobel Prize: Oil Drop Experiment for Measuring the Fundamental Unit of Electric Charge

PET acquisition and iterative reconstruction (basics in 6 minutes!)

PET acquisition and iterative reconstruction (basics in 6 minutes!)

Basics of least squares: modelling, predicting and reconstructing!

Basics of least squares: modelling, predicting and reconstructing!

How to undo convolution: deconvolution for image reconstruction (via Fourier & convolution theorem)

How to undo convolution: deconvolution for image reconstruction (via Fourier & convolution theorem)

Schrodinger's cat: did you ever really get it, and the link to quantum computing?

Schrodinger's cat: did you ever really get it, and the link to quantum computing?

Einstein's Nobel Prize: Photoelectric Effect

Einstein's Nobel Prize: Photoelectric Effect

Basics of k-space for MRI (magnetic resonance imaging)

Basics of k-space for MRI (magnetic resonance imaging)

Filtered backprojection (FBP) for image reconstruction: central section theorem, Radon & Fourier

Filtered backprojection (FBP) for image reconstruction: central section theorem, Radon & Fourier

Visualising 2D k-space and Fourier synthesis (1D & 2D, helps for image reconstruction and analysis)

Visualising 2D k-space and Fourier synthesis (1D & 2D, helps for image reconstruction and analysis)

Image reconstruction: sinograms, backprojected images, convolution, Radon & x-ray transform

Image reconstruction: sinograms, backprojected images, convolution, Radon & x-ray transform

Deep image prior: simple code for image restoration with no training data needed

Deep image prior: simple code for image restoration with no training data needed

AI vs. Physics in Image Reconstruction

AI vs. Physics in Image Reconstruction

Schrodinger equation: fast, simple mathematical description with consideration of the hydrogen atom

Schrodinger equation: fast, simple mathematical description with consideration of the hydrogen atom

Thomson's cathode ray tube: finding the charge to mass ratio of the electron

Thomson's cathode ray tube: finding the charge to mass ratio of the electron

Get started with convolutional neural networks (CNNs) to process an image - Jupyter Notebook/PyTorch

Get started with convolutional neural networks (CNNs) to process an image - Jupyter Notebook/PyTorch

Master your understanding of Fourier: basics to equations

Master your understanding of Fourier: basics to equations

Most remarkable formula in mathematics: Euler’s formula and expressions for cosine and sine

Most remarkable formula in mathematics: Euler’s formula and expressions for cosine and sine

Steepest Descent (Live Lecture)

Steepest Descent (Live Lecture)

Image reconstruction: FBP (filtered backprojection) basics, X-Ray Transform, Central Section Theorem

Image reconstruction: FBP (filtered backprojection) basics, X-Ray Transform, Central Section Theorem

Image reconstruction by deconvolution: least squares, Tikhonov regularisation & Gaussian likelihood

Image reconstruction by deconvolution: least squares, Tikhonov regularisation & Gaussian likelihood

Convolution equation explained simply in 3 forms: discrete, continuous and matrix-vector

Convolution equation explained simply in 3 forms: discrete, continuous and matrix-vector

Image reconstruction basics: vectors, matrices and manifolds

Image reconstruction basics: vectors, matrices and manifolds

PyTorch Principles for Deep Learning Iterative Reconstruction (Live recording, Elba, May 2022)

PyTorch Principles for Deep Learning Iterative Reconstruction (Live recording, Elba, May 2022)

Code for Deep Learned Filtered Backprojection (FBP) Image Reconstruction (PyTorch)

Code for Deep Learned Filtered Backprojection (FBP) Image Reconstruction (PyTorch)

Simple PyTorch code to put deep learning into iterative image reconstruction (embeds a CNN in MLEM)

Simple PyTorch code to put deep learning into iterative image reconstruction (embeds a CNN in MLEM)

Basics of AI for PET Image Reconstruction

Basics of AI for PET Image Reconstruction

Simple code for convolution and a CNN to denoise an image with real-time display in Python / PyTorch

Simple code for convolution and a CNN to denoise an image with real-time display in Python / PyTorch

Real-time CNNs to understand shift-equivariance, shift-variance, linearity and non-linearity

Real-time CNNs to understand shift-equivariance, shift-variance, linearity and non-linearity

Learning a convolution kernel to denoise or recover resolution

Learning a convolution kernel to denoise or recover resolution

Simple PYTHON code for iterative image reconstruction (also shown for a Jupyter notebook)

Simple PYTHON code for iterative image reconstruction (also shown for a Jupyter notebook)

Wave-particle duality: the wavefunction and quantum superposition

Wave-particle duality: the wavefunction and quantum superposition

Pt 4: Deep learned unrolled iterative image reconstruction

Pt 4: Deep learned unrolled iterative image reconstruction

Planck's constant: how to understand light quanta properly

Planck's constant: how to understand light quanta properly

Pt 3: Direct deep learned image reconstruction (PET, MR, CT examples)

Pt 3: Direct deep learned image reconstruction (PET, MR, CT examples)

Deep learning reconstruction: rapid summary of some recent work

Deep learning reconstruction: rapid summary of some recent work

Pt 2: Deep Learning Convolution, Feature Hierarchy Abstraction, Convolutional Neural Networks

Pt 2: Deep Learning Convolution, Feature Hierarchy Abstraction, Convolutional Neural Networks

Pt 1: Brief Reconstruction Review and Machine Learning Approach, Linear Model and FBP

Pt 1: Brief Reconstruction Review and Machine Learning Approach, Linear Model and FBP

Medical Image Reconstruction using Deep Learning (PRE-RECORDED version)

Medical Image Reconstruction using Deep Learning (PRE-RECORDED version)

Steepest descent least-squares optimisation - derivation explained (watch before conjugate gradient)

Steepest descent least-squares optimisation - derivation explained (watch before conjugate gradient)

Understanding convolution by imaging antimatter

Understanding convolution by imaging antimatter

Quick intro to convolutional neural networks for image processing in PET

Quick intro to convolutional neural networks for image processing in PET

Signals & Systems 2021: Signals and Multi-Dimensional Functions

Signals & Systems 2021: Signals and Multi-Dimensional Functions

Simple intro to high-dimensional vectors and manifolds

Simple intro to high-dimensional vectors and manifolds

Master your understanding of convolution: what it is and how to understand it well

Master your understanding of convolution: what it is and how to understand it well

Simple code for iterative image reconstruction (see https://youtu.be/IhETD4nSJec for PYTHON version)

Simple code for iterative image reconstruction (see https://youtu.be/IhETD4nSJec for PYTHON version)

Basic Iterative Image Reconstruction: Least Squares, Gaussian & Poisson Likelihood, Regularisation

Basic Iterative Image Reconstruction: Least Squares, Gaussian & Poisson Likelihood, Regularisation

Delta functions: Dirac delta and Kronecker delta for continuous and discrete function synthesis

Delta functions: Dirac delta and Kronecker delta for continuous and discrete function synthesis

Why Study Signals and Systems?

Why Study Signals and Systems?

Putting AI in the positron emission tomography (PET) imaging pipeline

Putting AI in the positron emission tomography (PET) imaging pipeline

PET-MR image reconstruction

PET-MR image reconstruction

The Size of the Atomic Nucleus

The Size of the Atomic Nucleus

Schrodinger Equation & Fourier Analysis: Quantum Superposition of Momentum States

Schrodinger Equation & Fourier Analysis: Quantum Superposition of Momentum States

Understanding the Fourier Transform (Analysis & Synthesis): Concepts to Equations

Understanding the Fourier Transform (Analysis & Synthesis): Concepts to Equations

Physics-Informed AI for Image Reconstruction in Positron Emission Tomography

Physics-Informed AI for Image Reconstruction in Positron Emission Tomography

Wave functions, the Schrodinger equation and example solutions

Wave functions, the Schrodinger equation and example solutions

Machine learning and deep learning for image reconstruction: PART 2 (direct and unrolled iterative)

Machine learning and deep learning for image reconstruction: PART 2 (direct and unrolled iterative)

Machine learning and deep learning for image reconstruction: PART 1 (convolutional neural networks)

Machine learning and deep learning for image reconstruction: PART 1 (convolutional neural networks)

The Fourier transform

The Fourier transform

Fourier series in 3 versions: summary and full visual demonstration

Fourier series in 3 versions: summary and full visual demonstration

Complex Fourier series, and postive and negative frequencies

Complex Fourier series, and postive and negative frequencies

Euler's formula (See NEW: https://youtu.be/DaK2ZSJNcFo), sin & cos in terms of complex exponentials

Euler's formula (See NEW: https://youtu.be/DaK2ZSJNcFo), sin & cos in terms of complex exponentials

Wave-particle duality: the wave function and superposition of states in the double-slit experiment

Wave-particle duality: the wave function and superposition of states in the double-slit experiment

Maximum a posteriori image reconstruction

Maximum a posteriori image reconstruction

The Bohr model of the atom

The Bohr model of the atom

Line spectra and the Rydberg formula

Line spectra and the Rydberg formula

Atomic models and how quantum physics began: blackbody radiation and the ultraviolet catastrophe

Atomic models and how quantum physics began: blackbody radiation and the ultraviolet catastrophe

Maximum likelihood – expectation maximisation & complete data: an understanding of the EM algorithm

Maximum likelihood – expectation maximisation & complete data: an understanding of the EM algorithm

Maximum likelihood – expectation maximisation (ML-EM) for real PET data

Maximum likelihood – expectation maximisation (ML-EM) for real PET data

Statistical image reconstruction: maximum Poisson likelihood for PET

Statistical image reconstruction: maximum Poisson likelihood for PET

Orthogonality of functions and vectors: key to Fourier analysis!

Orthogonality of functions and vectors: key to Fourier analysis!

Fourier series: how to find the coefficients (the amount of each sinuosoid)

Fourier series: how to find the coefficients (the amount of each sinuosoid)

Fourier series: simple demonstration of the principle

Fourier series: simple demonstration of the principle

The Fourier Series: getting into the basics of Fourier synthesis

The Fourier Series: getting into the basics of Fourier synthesis

Linear shift-invariance (LSI) and linear time-invariance (LTI)

Linear shift-invariance (LSI) and linear time-invariance (LTI)

Linear systems, linearity and non-linearity: what is linearity exactly?

Linear systems, linearity and non-linearity: what is linearity exactly?

Photoelectric effect: SEE NEWER: https://youtu.be/7r3D_XHb4L8

Photoelectric effect: SEE NEWER: https://youtu.be/7r3D_XHb4L8

Rutherford Scattering and the Atomic Nucleus

Rutherford Scattering and the Atomic Nucleus

Millikan's oil drop experiment: SEE NEW VERSION HERE: https://youtu.be/tEn5PvOByAU

Millikan's oil drop experiment: SEE NEW VERSION HERE: https://youtu.be/tEn5PvOByAU

Thomson's cathode ray tube experiment for finding the charge to mass ratio of the electron

Thomson's cathode ray tube experiment for finding the charge to mass ratio of the electron

Convolution in 1D and matrix-vector notation (time or space reversal of the kernel demystified!)

Convolution in 1D and matrix-vector notation (time or space reversal of the kernel demystified!)

Convolution in 2D

Convolution in 2D

Matrices and vectors: simple case of delta basis vectors

Matrices and vectors: simple case of delta basis vectors

Quick intro to convolution: linear shift-invariant (LSI) & linear time-invariant (LTI) systems

Quick intro to convolution: linear shift-invariant (LSI) & linear time-invariant (LTI) systems

Matrices and vectors: vector representation of a function or signal, matrix-vector multiplication

Matrices and vectors: vector representation of a function or signal, matrix-vector multiplication

Delta function representation of signals: part 2, 2D signals and images

Delta function representation of signals: part 2, 2D signals and images

Delta function representation of signals: part 1, 1D signals

Delta function representation of signals: part 1, 1D signals

Systems: defintion, examples for 1D and 2D signals

Systems: defintion, examples for 1D and 2D signals

Conjugate gradient method (watch steepest descent first: https://youtu.be/G0fv8nU8oPA)

Conjugate gradient method (watch steepest descent first: https://youtu.be/G0fv8nU8oPA)

Steepest Descent (SEE NEWER VIDEO: https://youtu.be/G0fv8nU8oPA ) - watch before Conjugate Gradient

Steepest Descent (SEE NEWER VIDEO: https://youtu.be/G0fv8nU8oPA ) - watch before Conjugate Gradient

Non-iterative & iterative reconstruction (II)P1: iterative least-squares, Landweber, SART, ART, ISRA

Non-iterative & iterative reconstruction (II)P1: iterative least-squares, Landweber, SART, ART, ISRA

Non-iterative and iterative image reconstruction methods Part 5

Non-iterative and iterative image reconstruction methods Part 5

Non-iterative and iterative image reconstruction methods Part 4

Non-iterative and iterative image reconstruction methods Part 4

Least-squares reconstructions for linear shift-variant systems, Tikhonov, and SVD inverse

Least-squares reconstructions for linear shift-variant systems, Tikhonov, and SVD inverse

Signals and Systems: Functions

Signals and Systems: Functions

Introduction to Signals and Systems

Introduction to Signals and Systems

Non-iterative and iterative image reconstruction methods Part 2

Non-iterative and iterative image reconstruction methods Part 2

Non-iterative and iterative image reconstruction methods: Part 1b

Non-iterative and iterative image reconstruction methods: Part 1b

Non-iterative and iterative image reconstruction methods Part 1a

Non-iterative and iterative image reconstruction methods Part 1a

Image Reconstruction: demo of Fourier analysis and synthesis (Fourier transform and inverse)

Image Reconstruction: demo of Fourier analysis and synthesis (Fourier transform and inverse)

Image Reconstruction: Convolution Theorem and Diagonalisation

Image Reconstruction: Convolution Theorem and Diagonalisation

Image Reconstruction: why the Fourier transform is crucial for understanding convolution

Image Reconstruction: why the Fourier transform is crucial for understanding convolution

Image Reconstruction: PET data, backprojection, sinograms, list-mode, convolution

Image Reconstruction: PET data, backprojection, sinograms, list-mode, convolution

Image Reconstruction: Linearity, Non-Linearity, Linear Shift-Invariance (Lec 2 of 6)

Image Reconstruction: Linearity, Non-Linearity, Linear Shift-Invariance (Lec 2 of 6)

Medical image reconstruction: images as high-dimensional vectors and use of matrices (Lec1 of 6)

Medical image reconstruction: images as high-dimensional vectors and use of matrices (Lec1 of 6)

AI in Image Reconstruction

AI in Image Reconstruction

AI for PET Image Reconstruction: Basic Principles

AI for PET Image Reconstruction: Basic Principles