Sparse representations are a foundational tool for modern signal processing and data analysis and have a wide range of applications, including denoising, compression, compressive sensing, classification etc. for a variety of signals including speech (audio), images, and video.
The course will focus on foundations of multi-resolution analysis and wavelet theory for sparse signal representation. Additionally, beyond the sparsity provided by fixed bases such as wavelets, the general framework of sparsity and structured sparsity will be presented. Emerging trends in sparsity for image analysis, that connect structured sparsity with deep learning principles (e.g. scattering networks) will also be introduced. The course will have a theoretical component as well as a hands-on project component where students will apply these techniques to a real-world image analysis problem.