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Compressed Sensing: When It Works
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Classroom Contents
Intro to Data Science
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- 1 Intro to Data Science: Overview
- 2 Intro to Data Science: Historical Context
- 3 Intro to Data Science: What is Data Science?
- 4 Intro to Data Science: Answering Questions with Data
- 5 Intro to Data Science: The Nature of Data
- 6 Machine Learning Overview
- 7 Machine Learning Goals
- 8 Machine Learning and Cross-Validation
- 9 Types of Machine Learning 1
- 10 Types of Machine Learning 2
- 11 Artificial Intelligence
- 12 Neural Network Overview
- 13 Neural Network Architectures & Deep Learning
- 14 Neural Networks and Deep Learning
- 15 Neural Networks: Caveats
- 16 Digital Twins
- 17 Data Visualization: Overview
- 18 Data Visualization: Types of Data
- 19 Data Visualization: Storytelling with Data
- 20 Data Visualization: Buyer Beware
- 21 Singular Value Decomposition (SVD): Overview
- 22 Singular Value Decomposition (SVD): Mathematical Overview
- 23 Singular Value Decomposition (SVD): Matrix Approximation
- 24 Singular Value Decomposition (SVD): Dominant Correlations
- 25 SVD Method of Snapshots
- 26 Matrix Completion and the Netflix Prize
- 27 Unitary Transformations
- 28 Linear Systems of Equations, Least Squares Regression, Pseudoinverse
- 29 Least Squares Regression and the SVD
- 30 Linear Systems of Equations
- 31 Linear Regression
- 32 Principal Component Analysis (PCA)
- 33 SVD and Optimal Truncation
- 34 SVD: Image Compression [Matlab]
- 35 SVD: Image Compression [Python]
- 36 Unitary Transformations and the SVD [Matlab]
- 37 Unitary Transformations and the SVD [Python]
- 38 Linear Regression 1 [Matlab]
- 39 Linear Regression 2 [Matlab]
- 40 Linear Regression 1 [Python]
- 41 Linear Regression 2 [Python]
- 42 Linear Regression 3 [Python]
- 43 SVD and Alignment: A Cautionary Tale
- 44 Principal Component Analysis (PCA) [Matlab]
- 45 Principal Component Analysis (PCA) 1 [Python]
- 46 Principal Component Analysis (PCA) 2 [Python]
- 47 SVD: Eigenfaces 1 [Matlab]
- 48 SVD: Eigenfaces 2 [Matlab]
- 49 SVD: Eigenfaces 3 [Matlab]
- 50 SVD: Eigenfaces 4 [Matlab]
- 51 SVD: Eigen Action Heros [Matlab]
- 52 SVD: Eigenfaces 3 [Python]
- 53 SVD: Eigenfaces 2 [Python]
- 54 SVD: Eigenfaces 1 [Python]
- 55 SVD: Optimal Truncation [Matlab]
- 56 SVD: Optimal Truncation [Python]
- 57 SVD: Importance of Alignment [Python]
- 58 SVD: Importance of Alignment [Matlab]
- 59 Randomized SVD Code [Matlab]
- 60 Randomized SVD Code [Python]
- 61 Randomized Singular Value Decomposition (SVD)
- 62 Randomized SVD: Power Iterations and Oversampling
- 63 Fourier Analysis: Overview
- 64 Fourier Series: Part 1
- 65 Fourier Series: Part 2
- 66 Inner Products in Hilbert Space
- 67 Complex Fourier Series
- 68 Fourier Series [Matlab]
- 69 Fourier Series [Python]
- 70 Fourier Series and Gibbs Phenomena [Matlab]
- 71 Fourier Series and Gibbs Phenomena [Python]
- 72 The Fourier Transform
- 73 The Fourier Transform and Derivatives
- 74 The Fourier Transform and Convolution Integrals
- 75 Parseval's Theorem
- 76 Solving the Heat Equation with the Fourier Transform
- 77 The Discrete Fourier Transform (DFT)
- 78 Computing the DFT Matrix
- 79 The Fast Fourier Transform (FFT)
- 80 The Fast Fourier Transform Algorithm
- 81 Denoising Data with FFT [Matlab]
- 82 Denoising Data with FFT [Python]
- 83 Computing Derivatives with FFT [Matlab]
- 84 Computing Derivatives with FFT [Python]
- 85 Solving PDEs with the FFT [Matlab]
- 86 Solving PDEs with the FFT [Python]
- 87 Why images are compressible: The Vastness of Image Space
- 88 What is Sparsity?
- 89 Sparsity and Parsimonious Models: Everything should be made as simple as possible, but no simpler
- 90 Compressed Sensing: Overview
- 91 Compressed Sensing: Mathematical Formulation
- 92 Compressed Sensing: When It Works
- 93 Sparsity and the L1 Norm
- 94 Solving PDEs with the FFT, Part 2 [Matlab]
- 95 Solving PDEs with the FFT, Part 2 [Python]
- 96 The Spectrogram and the Gabor Transform
- 97 Spectrogram Examples [Matlab]
- 98 Spectrogram Examples [Python]
- 99 Uncertainty Principles and the Fourier Transform
- 100 Wavelets and Multiresolution Analysis
- 101 Image Compression and the FFT
- 102 Sparse Sensor Placement Optimization for Reconstruction
- 103 Sparse Sensor Placement Optimization for Classification
- 104 Sparse Representation (for classification) with examples!
- 105 Image Compression with Wavelets (Examples in Python)
- 106 Image Compression with the FFT (Examples in Matlab)
- 107 Image Compression and Wavelets (Examples in Matlab)
- 108 Image Compression and the FFT (Examples in Python)
- 109 Beating Nyquist with Compressed Sensing, part 2
- 110 Underdetermined systems and compressed sensing [Matlab]
- 111 Underdetermined systems and compressed sensing [Python]
- 112 Beating Nyquist with Compressed Sensing
- 113 Robust Regression with the L1 Norm
- 114 Robust Regression with the L1 Norm [Matlab]
- 115 Robust Regression with the L1 Norm [Python]
- 116 Exponential Growth: Overview
- 117 Examples of Exponential Growth
- 118 Exponential Growth and Euler
- 119 Exponential Growth is a Lie
- 120 Machine Learning for Fluid Dynamics: Patterns
- 121 Machine Learning for Fluid Dynamics: Models and Control
- 122 The Anatomy of a Dynamical System
- 123 Beating Nyquist with Compressed Sensing, in Python
- 124 The Laplace Transform: A Generalized Fourier Transform
- 125 Laplace Transforms and Differential Equations
- 126 Laplace Transform Examples
- 127 Sparsity and Compression: An Overview
