There are many reasons for the popularity of Gaussian models. They are easy to deal with, lead to linear equations, and they have a strong theoretical justification given by the Central Limit theorem. However, many data manmade or natural exhibit characteristics too impulsive or skewed to be accommodated by the Gaussian model. The wide spread power laws in the nature, in internet, in linguistics, biology is very well known. In this talk we will challenge the „Normality“ of the Gaussian distribution and will discuss the alpha-stable distribution family which satisfy the generalised Central Limit Theorem. Alpha-Stable distributions have received wide interest in the signal processing community and became state of the art models for impulsive noise and internet traffic in the last 20 years since the influential paper of Nikias and Shao in 1993. We will provide the fundamental theory and discuss the rich class of statistics this family enables us to work with including fractional order statistics, log statistics and extreme value statistics. We will present some application areas where alpha-stable distributions had important success such as internet traffic modelling, SAR imaging, bioinformatics, astronomy, etc. We will identify the open problems which we hope will lead to fruitful discussion on further research on this family of distributions.
Ercan E. Kuruoglu was born in Ankara, Turkey in 1969. He obtained his BSc and MSc degrees both in Electrical and Electronics Engineering at Bilkent University in 1991 and 1993 and the MPhil and PhD degrees in Information Engineering at the Cambridge University, in the Signal Processing Laboratory, in 1995 and 1998 respectively. Upon graduation from Cambridge, he joined the Xerox Research Center in Cambridge as a permanent member of the Collaborative Multimedia Systems Group. In 2000, he was in INRIA-Sophia Antipolis as an ERCIM fellow. In 2002, he joined ISTI-CNR, Pisa as a permanent member. Since 2006, he is an Associate Professor and Senior Researcher. He was a visiting professor in Georgia Institute of Technology graduate program in Shanghai in 2007 and 2011. He was a visiting researcher/lecturer for extended periods in Bogazici University, Izmir Institute of Technology, Turkey, Institute of Physics-Cantabria, Spain, and Xidian University China. He is a 111 Bringing Foreign Experts to China Program Fellow and was a frequent visitor to Shanghai Jiao Tong University, China (2007-2011). He was an IEEE Visiting Professor in Hong Kong, in August 2012.
He is a recipient of the Alexander von Humboldt Foundation Fellowship (2012-2014) is currently a visiting scientist at Department of Theoretical Biophysics, Humboldt-Universität zu Berlin and Max-Planck Institute for Molecular Biology. He was an Associate Editor for IEEE Transactions on Signal Processing in 2002-2006 and for IEEE Transactions on Image Processing in 2005-2009. He is currently the Editor in Chief of Digital Signal Processing and also is in the editorial board of EURASIP Journal on Advances in Signal Processing. He was the Technical co-Chair for EUSIPCO 2006, he is the tutorials co-chair of ICASSP 2014. He served as an elected member of the IEEE Technical Committee on Signal Processing Theory and Methods (2004-2010), was a member of IEEE Ethics committee in 2012 and is a Senior Member of IEEE. He is the author of more than 100 peer reviewed publications and holds 5 US, European and Japanese patents. His research interests are in statistical signal processing and information and coding theory with applications in image processing, astronomy, geophysics, telecommunications, intelligent user interfaces and bioinformatics.