Research in this field is about multimedia signal processing for big data and coding for multimedia transmission. On the signal-processing side, the work particularly involves advanced methods for big data such as compressed sensing, iterative recovery algorithms in particular, as well as advanced machine learning, with applications, e.g., in image processing and communications.
Compressed Sensing (CS)
Compressed sensing is about (re-)sampling (digital) signals at a sampling rate far below the classical sampling theorem; perfect (or at least very high quality) recovery is still possible, with suitable structure (such as „sparsity“) in the signal. In practical applications (such as MRI scanners) the vector dimension of the signals can be very large (100000 and more), so extremely efficient recovery algorithms are crucial as well as good dictionaries to perform the sampling process, which is in fact a multiplication with a measurement matrix (the dictionary). Work items include fast recovery of very high-dimensional signals with different types of „structure“ (including „sparsity“) by iterative algorithms, in particular the application of approximate message passing (AMP) to problems in image processing but also in communications.
Machine Learning
Estimation of Information Measures: While information theoretic quantities such as entropy and mutual information are extensively used in the training and evaluation of machine learning systems, this usage is profoundly different from their applications in coding theorems. In the context of machine learning, these quantities need to be estimated. We investigate specifically adapted algorithms for this estimation problem, necessary conditions, and fundamental limitations.
Information Theory and Computability: In addition to the statistical properties of information measures, we analyze their computability in various models of computation. In particular, we consider information inequalities, the "rules" of information theory, as well as operational definitions of capacities and coding rates.
Coding
Error-correction channel coding has a key role in digital communication systems. Due to delay constraints of the applications, codes with small-to-medium block size are of particular interest. A special problem, which is very important in practice, is the realization of a flexible “adjustable” code rate, as time-variant fading channels necessarily require adaptive modulation and coding. We investigate Low-Density Parity-Check (LDPC) codes specifically constructed for those situations. A key problem of code design is to avoid short cycles in the code graph in order to allow for better decoding results. On the one hand we investigate code designs that avoid short cycles by construction, on the other hand we have introduced a transformation-based representation of quasi-cyclic LDPC codes that allows for a simple cycle analysis that can be used in numerical code design. We also consider extensions of those techniques to design codes with adjustable code rate.
Beyond the conceptual side of research in algorithms, we also work on implementing channel encoders and decoder by programmable hardware (FPGA, Field-Programmable Gate Arrays). The goal is a highly efficient realization of practically relevant LDPC channel encoders and decoders in order to investigate their performance at very low bit-error rates and to compare measurements with analytical results.
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. Our recent results in this area concern the integration of a classifier and of contextual information, as well as methods for probabilistic object association between sensors.
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. We also devised multi-object tracking algo- rithms 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.
Another line of our research is medical signal processing. Motivated by the fact that an analysis of the movement of arteries yields effective indicators for atherosclerosis, we developed a state-space model and a method for tracking the movement of the carotid artery based on an ultrasound video sequence. Our method achieves superior robustness to artifacts specific to the ultrasound modality by using a joint fusion-and-tracking approach that combines an optical flow algorithm with an unscented Kalman filter.
Signal processing methods are an essential part of several other research areas. For complementary signal processing research, see the sections Mobile Communications, Communication Theory, Flexible Wireless Systems, and Multimedia 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.
Modern communication systems (e.g., the mobile radio standard LTE Advanced) more and more rely on feedback channels to improve link quality. For this type of transmission with feedback we analyzed the maximum achievable information rates for the case where the feedback is quantized (as is always the case in practice due to rate limitations). We managed to show that contrary to noisy feedback linear encoding achieves non-vanishing rates. An extension of these results to multi-user systems led to the development of superposition codes, which enable an adaptation to the quality of the feedback signal and thereby maximize the transmission rate. We could solve the associated problem of determining the best resource allocation via algorithms for convex-concave optimization.
