Sparsity and Compression

This course introduces sparsity and compressed sensing for compression, optimization, and ill-posed inverse problems. It also covers L1-based robust regression, sparse classification, robust PCA, sensor placement, and model discovery with Python and MATLAB examples.

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.