EE4740 Sparse signal processing

Previous course name: Data compression: Entropy and sparsity perspectives

The course covers a comprehensive overview of compressed sensing. It introduces the notion of sparsity and gives an overview of the area of compressed sensing. It starts with the classical techniques to solve underdetermined linear systems. Then, the core problem of compressed sensing, namely the l0 norm minimization with linear constraints, is introduced. The compressed sensing problem is motivated using example applications from wireless communication, control, and image processing. The l0 norm is shown to be NP-hard, and several classical approximate algorithms like l1 norm minimization, orthogonal matching pursuit, and thresholding algorithms are discussed. Building on the classical solutions, more advanced solution techniques are then covered. The first approach is the sparse Bayesian framework that introduces general statistical tools such as majorization-maximization and expectation-maximization. The next state-of-the-art approach is the deep learning framework based on autoencoders and generative adversarial networks. This part closes with the theory of compressed sensing. Here, the mathematical concepts of spark, null space property, and restricted isometric property are introduced. Using these concepts and properties, the theoretical performance guarantees of the standard compressed sensing algorithms are studied. 

Learning objectives

At the end of the course, the student should be able to

1. Understand the concept of sparsity and compressive sensing from an optimization perspective.
2. Debate the functioning of different sparse recovery approaches, namely convex optimization, greedy, thresholding, Bayesian, and deep learning techniques. 
3. Discuss the theoretical underpinnings of sparse signal recovery and performance guarantees of compressed sensing algorithms.
4. Connect to recent literature on sparse signal recovery that builds upon the presented tools and techniques.

Although sufficiently independent, the course refers to EE4C03 Stat DSP, ET4386 Estimation and detection, EE4530 Applied convex opt.; SC 42140 Signal analysis & Learning-2D; SC 42150 Statistical SP.

Literature

1. S. Foucart, and H. Rauhut, “A mathematical introduction to compressive sensing,” Applied and Numerical Harmonic Analysis, Birkhäuser, New York, NY, (2013)

Teachers

Last modified: 2026-10-01