Digital Signal Processing with Kernel Methods

Preface

Why Did We Write This Book?

In 2001 we were finishing or had just finished our PhD theses in electronics and signal processing departments in Spain. Each of us worked with complicated and diverse datasets, ranging from the analysis of signals from patients in cooperation with hospitals, to satellite data imagery and antenna signals. All of us had grown in an academic environment where neural networks were at the core of machine learning, and our theses also dealt with them. However, support vector machines (SVMs) had just arrived, and we enthusiastically adopted them. We were probably the Spanish pioneers using them for signal processing. It took a bit to understand the fundamentals, but then everything became crystal clear. It was a clean notation, a neat methodology, often involved straightforward implementations, and admitted many alternatives and modifications. After understanding the SVM classification and regression algorithms (the two first ones that the kernel community delivered), we saw the enormous potential for writing other problems than maximum margin classifiers, and to accommodate the particularities of signal and image features and models.

First, we started to write down some support vector algorithms for problems using standard signal models, the ones that we liked most, such as spectral analysis, deconvolution, system identification, or signal interpolation. Some concepts from both the signal and the kernel worlds seemed to be naturally connected, ...