In this tutorial some basic linear algebra problems: basis change and projection, are discussed together examples of their applications in signal and image processing.

In typical linear algebra university courses perpendicular projections are only discussed. However, in image processing, e.g. for defining various color spaces, we need non-perpendicular projections. That is why this is the key problem in this tutorial.

This tutorial can be considered as the second part of a tutorial entitled “The Victory of Orthogonality”, given in 2020 by Professor Gilbert Strang at the 24th IEEE Signal Processing Algorithms, Architectures, Arrangements, and Applications (IEEE SPA) Conference, 23rd-25th September 2020, Poznań, Poland.

Instead, the motto of the present tutorial could be: “In captivity of non-orthogonality”.

Biography:

Adam Dąbrowski received the Ph.D. degree in Electrical Engineering (Electronics) from the Poznan University of Technology, Poznan, Poland in 1982. In 1989 he received the Habilitation degree in Telecommunications from the same university. Since 1997 he was a full professor in digital signal processing at the Faculty of Computing and then Faculty of Control, Robotics, and Electrical Engineering at Poznan University of Technology, Poland. Up to now he is Chief of the Division of Signal Processing and Electronics Systems. He was also professor at the Adam Mickiewicz University, Poznan, Poland, Technische Universität Berlin, Germany, Universität Kaiserslautern, Germany, visiting professor at the Eidgenössische Technische Hochschule Zürich, Switzerland, Katholieke Universiteit Leuven, Belgium and Ruhr-Universität Bochum, Germany. He was a Humboldt Foundation fellow at the Ruhr-Universität Bochum, Germany (1984-1986). He was Chairman of the Signal Processing and Circuits & Systems Chapters of the IEEE Poland Section and in the period 2020-2023 he was Chairman of the IEEE Poland Section.

Scientific interests of Professor Adam Dąbrowski concentrate on: digital signal processing (digital filters, signal separation, multidimensional systems, wavelet transformation), processing of images, video and audio, multimedia and intelligent vision systems, biometrics, and on processor architectures. He is author or co-author of 5 books and over 600 scientific and technical publications. Among them he is one of the co-authors of "The Computer Engineering Handbook" (first edition in 2002, second edition in 2008) bestseller and most frequently cited book of the CRC Press, Boca Raton, USA.