Скачать или смотреть Uri Ascher - The Lost Honour of l2-based Regularization

Uri Ascher presents as part of the UBC Department of Computer Science's Faculty Lecture Series, November 1, 2012.

In the past two decades, regularization methods based on the l1norm, including sparse wavelet representations and total variation, have become immensely popular. So much so, that we were led to consider the question whether l1-based techniques ought to altogether replace the simpler, faster and better known l2-based alternatives as the default approach to regularization techniques.

The occasionally tremendous advances of l1-based techniques are not in doubt. However, such techniques also have their limitations. Taking into account the considerable added hardship in calculating solutions of the resulting computational problems, l1-based techniques must offer substantial advantages to be worthwhile. Such is not always the case in our experience. In this talk we explore advantages and disadvantages of l1- compared to l2-based techniques using several practical case studies. Our results suggest that in many applications, l2-based recovery may still be preferred.