Harmonic Analysis for Signal Processing, Spring 2011

Harmonic Analysis for Signal Processing, Spring 2011

ECE 8823a: Harmonic Analysis for Signal Processing Spring 2011


ECE 8823a: Harmonic Analysis for Signal Processing

Spring 2011

Instructor

Justin Romberg, email:

Description

This course explores the influence of Harmonic Analysis in modern signal processing theory and applications. The major themes will be mathematical models for signals, sparse representations, and practical algorithms for signal processing applications.

Specific topics include: wavelets and time-frequency representations, approximation theory, best basis and sparse approximation, statistical estimation, compression, curvelets and geometrical decompositions for images, inverse problems, imaging, and compressed sensing.

We will approach these topics from both a mathematical and a practical standpoint, emphasizing fundamental bounds on performance and implementation of algorithms for applications.

Pre-requisites

ECE 6250 (Advanced Topics in DSP) or a solid understanding of linear algebra, familiarity with random processes, and basic knowledge of wavelets and time-frequency representations.

Download a syllabus (pdf)

Text

Much of the material in this course can be found in

A Wavelet Tour of Signal Processing, by S. Mallat  (Amazon)

The rest of the material will come from papers and lecture notes.

Topics

Basics of Hilbert spaces and representations in orthogonal bases

Basics of frames

Time-frequency representations

Wavelets

Sparsity and approximation theory

Statistical estimation of sparse signals (i.e. signal/image denoising)

Compression of sparse signals (i.e. image compression)

Geometrical decompositions for images

Inverse Problems: Recovering sparse signals

Compressive Sampling: Acquiring sparse signals