Weekly Seminar Series: “Compressed Sensing: Introduction to Theory and Practical Algorithms”
Compressed Sensing studies the compression and recovery of sparse signals with a reduced number of measurements. Efficient algorithms for reconstruction exists, such as the L1 minimization, many applications in signal processing (magnetic resonance images, sparse radar, face recognition, MIMO …), and the germinal papers of E.Candes, D.Donoho and T.Tao have led to the rapid development of a theory. The previous authors proved that a signal with a sparse representation could be recovered exactly with a small amount of linear measurements.
This course intends to establish the fundamental principles of the theory, to present some concrete applications in the field of signal theory, to discuss resolution algorithms and high-dimensional probabilistic methods for the initially raised problems.
The course will consist of 12 sessions of 2 hours divided into the following 3 blocks:
- First Block. Introduction.
- Introduction to compressed sensing.
- Discussion of some examples.
- Theoretical approach to the problem.
- Null Space property and RIP
- Coherence Conditions on the number of available measures. Bottleneck phenomenon. Randomness
- Second Block. Resolution algorithms.
- Greedy algorithms. MP. OMP.
- Descent of coordinates.
- Minimization and maximization algorithms and proximity methods.
- Structured sparsity.
- Third Block. Probabilistic techniques
- Motivation of probabilistic models.
- Gaussian models.
- Bounded orthonormal systems.
- Results of recovery in structured models.
- Future line of research and open problems.
May: Tuesday 29th
June: Tuesday 05th
Time: 11h to 13h
Carlos Buelga (Madrid, 1991) received his Bachelor and M.Sc degree in Mathematics from Universidad Complutense de Madrid (UCM), Madrid, in 2014-2015 respectively. He is currently studying his Ph.D. degree in signal theory in Universitat Politetècnica de Catalunya (UPC), Barcelona, Spain with a Ph.D. scholarship granted by MINECO. He is also part of communication system department at CTTC. His research interests are probabilistic aspects that appear across mathematics and various branches of data science, in particular, random matrix theory, free probability, geometric functional analysis, information theory, machine learning and compressed signal processing.
David Gregoratti received his M.Sc. degree in telecommunications engineering from “Politecnico di Torino,” Italy, in 2005, and his Ph.D. degree in signal theory and communications from “Universitat Politécnica de Catalunya” (UPC), Barcelona, Spain, in 2010. Since 2006 he is with the “Centre Tecnològic de Telecomunicacions de Catalunya” (CTTC), Barcelona, Spain, first as a Ph.D. Candidate and now as a Research Associate in the Advanced Signal and Information Processing Department. During his academic career, he also visited “Institut Eurecom” (Sophia Antipolis, France, in 2003–2004), “Qualcomm Inc.” (San Diego, CA, USA, in 2004), “Telecom Italia LAB” (Torino, Italy, in 2005) and “Télécom ParisTech” (Paris, France, in 2009). Dr. Gregoratti has been actively participating in diverse research projects (with both public and private funding) as well as in the organization of IEEE-sponsored events. His current research interests cover wireless communications, multicarrier modulations and optimization with sparsity.