Lecture Image and Geometry Processing II:

Numerical Methods in Signal and Image Processing

Summer term 2021

Lecture
Tuesdays, 10:15 - 11:55, online
Fridays, 10:15 - 11:45, online
First lecture: 13 April 2021

Exercises
3 groups (online)
The exercise course starts in the second week with some material additional to the lecture.

Participants:
The lecture is suitable for students in mathematics, physics and computer science.

Assumptions to finish the lecture successfully:
There will be oral examinations (20 minutes) in summer.

Assumptions to get admission for the examination:
Attendance of the exercises, presentation of two exercise solutions, and 50 percent of the achievable points for homework.
With this lecture + exercises you can obtain 9 ECTS points.

Content:
This Lecture Image and Geometry Processing II is concerned with numerical methods for image compression and image denoising. In particular we will focus on the following topics:

1. Introduction

2. Compression of signals and images
2.1 Criteria for image compression
2.2 Data reduction
2.3 Encoding (Huffman-encoding)
2.4 Decorrelation using trigonometric transforms
2.5 Functionality of JPEG
2.6 Compression using wavelet filter banks

3. Image restoration and image denoising
3.1 Introduction: Summary of different methods for image denoising
3.2 Image denoising using nonlinear diffusion filtering
3.3 Regularization methods for image denoising

Literature:

K. Bredies, D. Lorenz, Mathematical Image Processing, Birkhäuser, 2018.
B. Jähne, Digitale Bildverarbeitung, Springer, 6. Edition, 2005.
S.D. Stearns, D.R. Hush, Digitale Verarbeitung analoger Signale, R. Oldenbourg Verlag München, 1994.
A.V. Oppenheim, R.W. Schafer, Digital Signal Processing, Englewood Cliffs, Prentice Hall, 1975.
S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 3. edition, San Diego, 2009.
R.C. Gonzalez, R.E. Woods, Digital Image Processing, Addison-Wesley, New York, third edition, 2008.
J. Weickert, Anisotropic Diffusion in Image Processing, Teubner, Stuttgart, 1998.