This course aims to teach learners about sparsity and compression in various data types, with a focus on images. By the end of the course, students will understand the concepts of sparsity, compressed sensing, and the mathematical formulations behind them. They will also learn practical skills such as working with underdetermined systems in Python and Matlab, implementing compressed sensing techniques, and using tools like PySINDy for model discovery. The teaching method includes theoretical explanations, mathematical formulations, coding exercises, and practical examples. This course is intended for individuals interested in data compression, signal processing, image processing, and those looking to enhance their skills in mathematical modeling and data analysis.
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
