This integrated course aims at teaching advanced signal processing methods for combining signal and data treatment with theoretical modeling, as well as for implementation of different methods and algorithms for data-mining and classification. The objective is to improve the relevant information obtainable in Medicine for both physiological and clinical purposes through the application of these advanced methodological and processing tools. The course covers the fundamentals of less traditional, advanced approaches aimed at improving medical diagnosis, treatment and rehabilitation. Each topic is treated both theoretically and practically, with pivotal examples relative to the neural and cardiovascular systems, focusing on the central and peripheral autonomic nervous system.

Students will be able to understand, design, and implement advanced signals and data processing algorithms and mathematical tools in the context of Medicine and Biology.

In particular, students will learn how to:

• Identify a specific problem in dealing with targeted medical information and apply the most suitable algorithm among the various ones explained in the course.
• Evaluate the pros and cons of alternative approaches with respect to more established ones. Identify specific classes of common problems in biomedical information processing in a wide range of applications for different systems or organs, at various scales of investigation. Be skilled enough to properly manage and apply advanced methods and algorithms like time-frequency and time-scale distributions, deterministic chaotic time series, higher order analysis, etc.
• Properly manage and apply advanced methods and algorithms in order to perform statistical analysis and modeling, multivariate and nonlinear signal processing, regression and classification from evenly and unevenly sampled time series.
• Understand various complex physiological and clinical settings from the standpoint of information detection and classification

Part I

Methods. From deterministic to stochastic filtering. Recursive and non-recursive estimators. Optimal estimators. Optimal filters and parametric identification: Wiener filters and Kalman filters. Adaptive filters. Time-variant parametric methods. Time-frequency analysis, time-scale and wavelet analysis. Linear approach and quadratic distributions. Complexity of biomedical systems and signals: basic definitions of systems with non-linear dynamics. Higher order analysis of biomedical signals: bispectrum and bicoherence. A new approach for the processing of biomedical information: "multi"-paradigm. Integration of the information in multivariate, multiorgan, multimodal and multiscale approaches: fusion of the information across the single scales.

Applications. Relative mainly to the studying of Central Nervous System, of the Autonomous Nervous System, of the Cardiovascular System, of the Respiratory system and their interactions.

Part II

Methods. Introduction to Information Theory. Statistical modeling: Bayes' rule, State-Space Models, Point Process Models. Blind source separation: Use of principal component analysis (PCA) and independent component analysis (ICA) for filtering. Multivariate Causality and Higher Order Spectra. Highlights on Statistical Learning and Data Mining. Regression and Classification. Machine Learning: Graph Search, Constraint Satisfaction, Nearest Neighbors, Decision Trees, Neural Networks, Support Vector Machines. Unsupervised Learning.

Applications. Unraveling the Neural Code. Neural and Cardiovascular Point Process Models. EEG and MEG Blind Source Separation. Higher order analysis of cardiorespiratory signals and EEG recordings. Physiological Brain Correlates: Combining Brain Imaging techniques with Physiological variables. Classification: USA arrest data, the Heart Data example, gene expression data, breast cancer microarray study.

At the time of attendance, students are required to be familiar with the basic principles, methods and algorithms of biomedical signal and data processing. These topics are generally provided inside a course at the Bachelor Degree, or propedeutic to an advanced course on signal processing.

The evaluation will be given on the basis of an oral exam, covering the topics dealt with during the Lessons and Exercise hours of the two Parts [1][2] (Advanced Signals and Data Processing in Medicine) which constitute integrant parts of the Course. The Student may choose to take the exam relative to only one Part of the Integrated Course, provided that he/she passes the other Part of the Course within the Sessions of the Academic Year of attendance. The exam is passed if the Student gets a positive evaluation in both Parts. The final grade is the average of the single grades obtained from the two parts.