Signal Processing
The development of statistical signal processing methods for multi-object tracking in centralized and decentralized scenarios is a major focus of our work. An example is the task of detecting vehicles and estimating their time-varying positions based on data provided by sensing devices such as radar, sonar, or cameras. Distributed algorithms for decentralized sensor networks have the advantage of not requiring a central processing unit or communication between distant sensors. We are mainly interested in the challenging case where the number of objects and the association between measurements and objects are unknown.
A notable outcome of our research has been the introduction of factor graphs and the belief propagation algorithm to the field of multi-object tracking. The belief propagation approach is advantageous because of its superior efficiency, scalability, and versatility. Our belief propagation-based multi-object tracking algorithms are able to fuse the measurements of multiple sensors and to continually adapt to time-varying system parameters. Our most recent results in this direction include methods for integration of contextual information and for probabilistic object association between sensors.
We also devised multi-object tracking algorithms in which the object states and the measurements are modeled by finite point processes. In particular, the use of marked finite point processes enables the estimation of entire object trajectories with consistent identification of the objects. We were able to achieve a superior performance–complexity compromise through a judicious combination of marked and non-marked finite point processes.
Another line of our research is the estimation of the optical flow, which is an important problem in image processing with a wide range of applications including video compression, autonomous navigation, and medical diagnosis. We proposed a unified statistical methodology for optical flow estimation that is based on a variational bound. Our approach is well suited to ultrasonic imaging as it supports ultrasound-specific statistical models.
Signal processing methods are an essential part of several other research areas. For complementary signal processing research, see the sections Mobile Communications, Communication Theory and Flexible Wireless Systems.
Communication Theory
The focus of our research is on wireless communication and sensor networks and on signal processing for Big Data.
The young field of graph signal processing is being successfully applied for the analysis of datasets from social networks, communication networks, infrastructure networks, biological networks, and multimedia. In this area, we developed methods for the reconstruction of missing data points in sampled graphed signals. As a metric for the smoothness of the graph signal we used the total variation induced by the underlying graph. This led to non-smooth minimization problems, which we solved using modern methods of convex optimization. The resulting algorithms are computationally efficient and suited for distributed implementation, which enables the practical applications to massive datasets. We could verify the excellent performance of our scheme using a real-world dataset of Amazon products and ratings.
We furthermore considered the problem of learning the structure of a graph from huge but possibly incomplete and noisy data sets distributed implementations. We formulated this problem as a quadratic optimization problem and we proposed to solve this problem using an efficient implementation of the ADMM algorithm that scales linearly with the number of data points and thus is well-suited for large-scale data. Numerical experiments with real-world data confirmed the excellent performance of our method. Among other things we managed to determine the party affiliation of Austrian Members of Parliament from anonymous voting results in the Austrian National Council.
Another key focus of our work in the area of graph signal processing was the problem of clustering, i.e., grouping data points such that groups are maximally homogeneous (points within a group are similar) whereas distinct groups are as much separated as possible (points in distinct groups are maximally dissimilar). For this purpose, we developed methods that build on signed graphs and use either the graph spectrum or total variation minimization to determine the data clusters. For the latter we were able to prove that in the majority of cases the clustering results coincide with the optimal but numerically intractable graph cut.
In cooperation with École Polytechnique Fédérale de Lausanne (EPFL, Switzerland) we explored efficient decoder architectures for low-density parity check (LDPC) codes. More specifically, we devised quantized message passing algorithms that maximize the information flow in the code graph and particularly well suited for hardware realization. The synthesis of a decoder for 10GigabitEthernet in 28nm CMOS technology lead to a record-breaking throughput of more than 500 Gigabit per second at 20mm2 chip area.