Explore the concepts of sparsity and compression in this comprehensive 4.5-hour video series. Delve into the vastness of image space, understand the fundamentals of compressed sensing, and learn how to beat the Nyquist sampling theorem. Discover the power of the L1 norm in robust regression and sparse representation for classification. Investigate advanced topics such as Robust Principal Component Analysis (RPCA) and sparse sensor placement optimization. Gain practical skills using Python and MATLAB to implement underdetermined systems, compressed sensing, and robust regression techniques. Examine the importance of parsimonious models and explore PySINDy, a Python library for model discovery. Master the art of creating simple yet effective models in data analysis and signal processing.
Overview
Syllabus
Why images are compressible: The Vastness of Image Space.
What is Sparsity?.
Compressed Sensing: Overview.
Compressed Sensing: Mathematical Formulation.
Underdetermined systems and compressed sensing [Python].
Underdetermined systems and compressed sensing [Matlab].
Beating Nyquist with Compressed Sensing.
Shannon Nyquist Sampling Theorem.
Beating Nyquist with Compressed Sensing, part 2.
Beating Nyquist with Compressed Sensing, in Python.
Sparsity and the L1 Norm.
Compressed Sensing: When It Works.
Robust Regression with the L1 Norm.
Robust Regression with the L1 Norm [Matlab].
Robust Regression with the L1 Norm [Python].
Robust, Interpretable Statistical Models: Sparse Regression with the LASSO.
Sparse Representation (for classification) with examples!.
Robust Principal Component Analysis (RPCA).
Robust Modal Decompositions for Fluid Flows.
Sparse Sensor Placement Optimization for Reconstruction.
Sparse Sensor Placement Optimization for Classification.
Sparsity and Parsimonious Models: Everything should be made as simple as possible, but no simpler.
PySINDy: A Python Library for Model Discovery.
Taught by
Steve Brunton
