Tools for complex systems
We focus on computational tools as well as their applications to analyze and understand interactions between parts of a complex system and the overall complex system. From such analysis, we aid the decisions of choosing suitable parameters/models, optimizing and guarantee system performance. To this end, we study and develop advanced mathematical tools as well as adaptive algorithms to design and model real-world systems efficiently in bio-medicine, electronics and telecommunication.
Our current research topics include adaptive matrix and tensor analysis, system identification, statistical performance analysis of communication systems and artificial intelligence for communication systems.
Core members
Dr. Le Trung Thanh, Group leader
Prof. Karim Abed-Meraim, International advisor
Assoc. Prof. Nguyen Linh Trung
Signal and image data stream analytics: From subspace to tensor tracking
Stream processing has recently attracted much attention from both academia and industry since massive data streams have been increasingly collected over the years. This project focuses on investigating the problem of online low-rank approximation (LRA) of data streams over time. When data samples are one-dimensional, the online LRA problem is referred to as subspace tracking. It turns out to be tensor tracking when streaming data are multi-dimensional.
Tensor-based methods for source separation
Source separation (SS) is a signal processing technique that aims to separate a set of mixed signals into their source components without prior knowledge about the sources or the mixing process. In other words, SS methods seek to detect the individual sources from their observed linear combinations, referred to as mixed signals or observations. This problem is considered “blind” when it does not rely on any information about the sources or the mixing system, making it a challenging task. Blind SS or BSS has already found applications in various fields such as telecommunications, audio processing, medical signal analysis, and more. In parallel, tensor decomposition (TD), a powerful mathematical technique, involves breaking down multi-dimensional arrays, known as tensors, into simpler components. Accordingly, The versatility of TD makes it a valuable tool for extracting meaningful insights from high-dimensional data in diverse scientific and technological applications. In this project, we investigate the problem of blind source separation (BSS) through the lens of tensor decomposition (TD). Several fundamental connections between TD and BSS are established, forming the basis for novel tensor-based BSS methods.
Adaptive matrix and tensor analysis
Large volumes of data are being generated at any given time, especially from transactional databases, multimedia content, social media, and applications of sensor networks. When the size of datasets is beyond the ability of typical database software tools to capture, store, manage, and analyze, we face the phenomenon of big data for which new and smarter data analytic tools are required. Big data provides opportunities for new form of data analytics, resulting in substantial productivity. We explore fast (adaptive) matrix and tensor decompositions as computational tools to process and analyze multidimensional massive-data (with a focus on streaming data). We consider some real-world problems such as Radio Frequency Interference (RFI) Mitigation in radio astronomy or monitoring long and multi-channel EEG data.
Informed system identification
System identification (SI) is necessary in many applications such as control, telecommunication, biomedical signal processing, to name a few, to understand and control the behavior of the considered system. In particular, in the inverse problems it is required to identify the relation between the output and input signals of the system in order to restore or extract some information on the latter. In many situations, one has to handle the identification problem using only the system output signal in addition to structural or statistical information about the system and its inputs. This is referred to as the problem of blind SI. We are interested in “informed” SI, where we have more information to handle the limitation of blind SI. Various types of information are to be considered, such as side information or information obtained from a learning process.
Statistical performance analysis of telecommunication systems
We use tools from statistics, probability theory and stochastic processes to achieve performance bounds for communication systems of interest. Then, parameters of system configuration can be optimized to reach optimal performance.
Other information
Contact: Dr. Le Trung Thanh