In the build up to ICASSP 2020 we asked Petar Djuric and Cédric Richard about Cooperative and Graph Signal Processing and their book Cooperative and Graph Signal Processing: Principles and Applications on the topic:

• How long have you been researching Cooperative and Graph Signal Processing?

Petar: I have been working in cooperative and graph signal processing for almost two decades. First, I got interested in distributed particle filters and then on distributed sensor self-localization in wireless sensor networks. My work in cooperative signal processing continued to grow by engaging in consensus-based methods and particle filtering and distributed Bayesian learning in multiagent systems. These days, my interest is making inference about interacting systems from graph signals.

Cédric: I started working in this field in 2009, with the advent of sensor networks and diffusion adaptation algorithms, but this theme became a priority for me in 2013.

• What got you interested in researching into these areas?

Petar: The intellectual challenges that these areas of research offer were the main reason for getting involved in them. It is also very pleasing that the number of possible applications of cooperative and graph signal processing is very large. Understanding some of the basic principles that take place in complex systems where cooperation takes place is a great reward to any researcher.  

Cédric: Signal processing over wireless sensor networks started to be a hot research topic in the mid 2000’s. The initial motivation of my group and I was to deploy and test algorithms on MICAz motes to obtain a working knowledge in the implementation of wireless sensor networks for environmental monitoring applications.

• Why are these topics having such an impact?

Petar: Perhaps the main reason is that we are surrounded by complex systems, which are created by nature, society, or are simply engineered and that are difficult to grasp. Obviously, there can be great benefits if one understands these systems, their dynamics, structure, and interconnections. In engineering, one can design better systems, and in social and natural sciences one can influence systems to prevent unwanted outcomes. A very good example of a complex system is the brain, whose workings remain still quite mysterious. The theory of cooperative and graph signal processing provides venues for making a number of inroads in neuroscience, for example, understanding the coordinated activity in the brain that corresponds to perception, action, and/or behaviour.

Cédric: Recent years have witnessed an explosion of interest in processing massive datasets, owing notably to a large variety of applications. A wide spectrum of data processing problems are network-structured and require adaptation to time-varying dynamics. Sensor networks, social networks, vehicular networks, communication networks, and power grids are some typical examples. Signal processing over networks and graphs has provided a powerful and convenient set of tools for such scenarios, allowing for efficient in-network learning and adaptation. Network models have also provided useful ways to define the relationships between physical data collection, storage and processing units as well as data repartition and dependence. 

• You have edited a book entitled: Cooperative and Graph Signal Processing: Principles and Applications. What was your objective in developing this book?

Petar: The objective of this project was to create an educational resource for research and instruction for a broad audience, which includes both beginners and experts and many in-between. Besides introducing the basics of cooperative and graph signal processing, the book has also solid ties to some very important areas where the theory is applied including communications and social networks. Applications are also emphasized such as big data, the Internet-of-Things, and brain networks.

Cédric: Our objective was to provide the fundamentals of signal processing over networks, to present the latest advances in graph signal processing, and mix theories with practical applications. These areas have grown considerably in the past few years. This growth can be attested by the introduction of new journals in this field, the increased number of submitted and published articles, and the large number of special sessions at conferences and workshops. This book demonstrates the essential role that signal processing has in the field of network science.

• What approach does it take and how will it benefit researchers and students interested in these areas?

Petar: The book has five parts of which the first two are devoted to explaining the fundamental principles of inference over networks (Part 1) and of signal processing on graphs (Part 2). Each of these parts are composed of self-contained chapters that provide readers with fairly quick introduction in this field. A good approach to using the book is to go through relevant chapter(s) of the first two parts. Then, one can proceed by reading chapters of interest from the remaining three parts, which are on applications in communications, networking and sensing (Part 3), social networks (Part 4) and other applications (Part 5). 

Cédric: The book provides the basics of signal processing over networks as it applies to network science. Then, it brings to the forefront chapters on graph signal processing, which generalizes the well-known one- and two-dimensional signal processing. The book also covers two important areas, one on distributed communications and the other on social networks. Finally, the book also has chapters on applications, including media and video, smart grids, big data, the Internet of Things, and wireless health.

• How do you see these areas developing in the next few years?

Petar: Cooperative and Graph Signal Processing are areas that will continue to evolve and flourish. Their importance is attested by regular solicitations for research proposals in these domains issued by many agencies around the world. Clearly, much of the research will be driven by applications. A good number of these applications will be related to artificial intelligence whereas others will be dealing with big data. Recently, for example, federated learning has emerged as an interesting research direction where the objective is that agents collaborate to learn a shared model while using private training data. 

Cédric: Many government agencies, research institutions, and companies are embracing automation relying on a variety of sensing devices and infrastructure to collect, store, and process data on a continuous basis. The resulting vast amounts of raw data, produced from diverse sources, already surpass the analysis and decision-making capabilities of many existing frameworks, thus calling for new breakthroughs in data science. Within this context  

• For anyone thinking of developing a graduate course covering either of these areas, do you have any suggestions?

Petar: The title of the book may suggest that its chapters contain topics from two areas, cooperative signal processing and graph signal processing. One certainly may easily design courses with a focus on these themes and there are plenty of nice chapters to choose from for such courses. For these courses, there is a good mix of chapters with fundamentals and chapters that are on more advanced subjects. Further, one can use the book to have one single graduate course which will be on a generic subject like inference on graphs. Or it can be a textbook for a course on social networks or a course on distributed communications, networking and sensing. The book also contains several chapters that are focused on specific application areas. Thus, another course could be on applications of signal and information processing over networks. In summary, the book is a treasure-trove for developing a range of graduate courses, from basic courses to more advanced ones.  

• What do you think are the research challenges for researchers wanting to develop these areas further?

Petar:   There are plenty of challenging problems on basically every topic addressed by the individual chapters of the book. In general, however, one could argue that the main challenges are the extraction of accurate information from big data that describe a complex system which in turn are represented by networks or graphs. To that end, of increased interest are data driven methods for inference with emphasis on deep learning.

• For someone new to researching these areas, what tips can you give them?

Petar:    Those who are new to these areas must make sure that they have good fundamentals before they start researching the areas. The fundamentals besides calculus, linear algebra, and basics of graph theory include signals and systems, probability and random processes, estimation and detection theory, and machine learning. 

 About the book:

• Presents the first book on cooperative signal processing and graph signal processing
• Provides a range of applications and application areas that are thoroughly covered
• Includes an editor in chief and associate editor from the IEEE Transactions on Signal Processing and Information Processing over Networks who have recruited top contributors for the book

The book is available now on ScienceDirect. Want your own copy? Enter STC320 when you order via the Elsevier store to save up to 30%