This free one-day online workshop in English, intended for students, scientists, and programmers working in data analysis and artificial intelligence, will be held on Friday, November 29, 2024, from 9:30-14 (CET) (including a one-hour break).

The participants should know programming and linear algebra (including eigenvalues and singular values and vectors). Familiarity with signals and linear programming is a plus, as is some familiarity with Julia and Pluto notebooks.

The lecture materials are reactive Pluto notebooks in Julia language which will be available on GitHub.

During the workshop, we will cover three algorithms used in signal processing and data analysis. The algorithms use methods of linear algebra to solve the following problems:

1. Signal Decomposition

Input: Suppose we are given a data signal that consists of several nearly mono-components (almost periodic signal where amplitude, frequency, and phase slightly change in time). 
Question: Can we recover the mono-components? 
Answer: YES, with an efficient algorithm using fast eigenvalue decomposition of Hankel matrices!
Applications: Mono-component recovery can be successfully used to analyze audio signals.

2. Sparse + Low-rank Splitting

Input: Suppose we are given a data matrix, and know that it has a form A=L+S, where L is a matrix of low rank and S is a sparse matrix 
(but we know neither the rank nor the location of the non-zero entries).
Question: Can we recover L and S?
Answer: YES, with high probability using an efficient algorithm based on singular value decomposition and iterative thresholding!
Applications: Detecting moving objects in video surveillance, latent semantic indexing, collaborative filtering.

3. Compressive Sensing

Input: Several samples of a sparse signal. The number of samples is (far) smaller than the desired signal resolution. 
Question: Can we recover the sparse signal from a few measurements?
Answer: YES, for some signals and carefully selected measurements using l1 minimization (linear programming)!
Applications: Images. 

Learning Outcomes:
Upon completion, the participants will be able to:

- use Julia and Pluto notebooks,
- recognize applications where signal decomposition into mono-components can be efficiently used and use it,
- apply sparse-plus-low-rank splitting to video streams,
- apply compressive sensing to image transformations.

Registration: 

Participation is free of charge, but the registration, open until November 28., 2024., is required at https://docs.google.com/forms/d/e/1FAIpQLSd_2CH899dIUJiZ_kOPR3OOJXz0sk5qO5n7cxVvS5djlfNE0Q/viewform

The maximal number of participants is limited. Confirmation of attendance with meeting link will be sent by e-mail.

Instructor: Prof. dr. sc. Ivan Slapničar, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture

Organizers:

University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture (https://www.fesb.unist.hr/) and The Croatian Competence Centre for HPC (https://www.hpc-cc.hr/) within  EuroCC2 project (Contact: eurocc@fesb.hr)