**Signal Processing**

### Cognitive Networks

Studies on herding in economics and the social and biological sciences have observed that coordination among multiple agents leads to regular patterns of behavior and swarm intelligence, even when each group member shows very limited behavioral complexity. Can one explain how and why such manifestations of rational behavior arise at the group level from the interactions of agents with limited individual abilities at the local level? What communication topologies enable such behavior and how much information quantization is performed at the local level? Our research proposes to exploit the connection between socio-economic-biological networks and cognitive networks in an effort to understand and reverse-engineer the decentralized intelligence encountered in the biological and socio-economic domains. What distinguishes this work from prior efforts is its focus on understanding how learning and rationality evolve from low-level interactions on one hand, and how network dynamics and mobility relate to optimality on the other hand. Learn more.

### Global Behavior

We consider fusion of information collected by a large scale, distributed, sparsely connected network of sensing agents, sensing centers, or sensors monitoring a large collection of dynamical (possibly stochastic) sparsely coupled systems. Examples include large critical infrastructures such as the power grid, the telecom wireless infrastructure, or an information network. We develop new methodologies to study the global behavior of these large scale networked systems that emerges from a multitude of local actions (events) and to study fusion (e.g., detection, estimation) under their prevailing operation conditions, e.g., besides measurement and communication noise, the intermittency of infrastructure failures. Learn more.

### Sensor Networks

The potential for large-scale surveillance systems has attracted attention in recent years due to emerging technological advancements. The increasing levels of integration as well as the development of robust signal processing algorithms lend themselves to the deployment of affordable yet reliable sensing systems, which are envisioned as networks of autonomous densely distributed sensor nodes. Power and bandwidth scarcities make the design of such networks a delicate task, involving a careful balance between competing goals and objectives, which has been the subject of research from a variety of perspectives. One viewpoint emphasizes the communication and networking issues such as, routing protocols, networking architectures, and transmission technologies. Our viewpoint focuses on distributed inference algorithms like detection, estimation, localization. Learn more.

### Time Reversal Imaging Laboratory (TriLab)

Time reversal techniques obtain increased resolution by exploiting scattering and multipath in propagation through inhomogeneous channels. Time reversal has been used by Fink and collaborators to achieve super-resolution focusing in acoustics, [Fink, Prada, Wu, Cassereau, 1989,Fink, 1997] as demonstrated by their work with controlled ultrasonic experiments in water tanks. More recently large-scale acoustics experiments in the ocean have confirmed the resolution ability of time reversal, [Kuperman, Hodgkiss, and Song, 1998,Song, Kuperman, Hodgkiss, Akal, and Ferla, 1999]. In our work, we study matched field detection with time reversal in the electromagentic (EM) domain. Learn more.

### Time Reversal: Infrastructure Health Monitoring

Ultrasonic guided wave technology has become an important tool for evaluating the integrity of structures. Guided waves can travel long distances in many materials and propagate through the entire thickness of the object under test. These properties make them appealing for nondestructive inspection. In a structural health monitoring environment, transducers are permanently attached to the structure. These systems can be used to monitoring large networks of pipelines in real-time. Processing techniques can also take advantage of the transducers’ spatial diversity to improve detection performance, while reducing power requirements. We have demonstrated a monitoring technique using Time Reversal Change Focusing (TRCF). Learn more.**Algebraic Signal Processing and Transforms**

### DSP on Graphs

We are interested in developing digital signal processing concepts like the Fourier transform, filtering, spectrum for signals that are indexed by arbitrary graphs. This builds on the algebraic signal processing, part of a previous project, called SMART. Learn more.

### SMART

Many algorithms in digital signal processing are based on the use of linear discrete signal transforms. Mathematically, such a transform is a matrix-vector multiplication y=M .x where x is the sampled signal, and M is the transform over some base field K. Crucial for the applicability of a signal transform M is the existence of fast algorithms that allow its computation with O(n\log n) operations (or better) compared to O(n^2) arising from a direct matrix-vector multiplication. The problem of finding these algorithms for different transforms has been a major research topic leading to a vast number of publications in signal processing and mathematics. In SMART, we present an algebraic approach to the class of the 16 trigonometric transforms in the framework of algebra representation theory. Learn more.

### SPIRAL

With the growing complexity and diversity of computer platforms, the design of high-performance software implementations of digital signal processing (DSP) algorithms has become an increasingly more difficult task. When high performance is an issue, the designers have to fine tune software implementations to utilize the specific features of the target platform. This requires expert knowledge in both algorithm development and computer architecture, and the hand-coding of the implementations becomes a tedious and time-consuming task. Furthermore, the ever-changing hardware and compiler technology requires frequent re-implementation, since the platforms are often changed or upgraded. These problems are tackled by what are commonly known as automatic software performance tuning systems, which are automatically adapting software implementations to a wide range of platforms. Because of the complexity of the problem, most performance tuning systems implement only basic functions that are used as building blocks in more complex applications. There is a growing interest in automatic tuning of DSP algorithms since DSP applications typically require high-performance algorithm implementations. Learn more.**Bioimaging**

### Magnetic Resonance Imaging

Our work in Bioimaging develops signal and image processing methods for post-processing of magnetic resonance imaging (MRI) sequences of transplanted organs in humans and small animal models (rats). We work in close collaboration with the NMR Center for Biological Sciences, a NIH supported Center. We process kidney and heart perfusion MRI data, and tagged and untagged cardiac data. Learn more.**Communications**

### LDPC and Turbo Codes

Low-density parity-check (LDPC) codes were originally introduced in his doctoral thesis by Gallager in 1961. Since the discovery of Turbo codes in 1993 by Berrou, Glavieux, and Thitimajshima, and the rediscovery of LDPC codes by Mackay and Neal in 1995, there has been renewed interest in Turbo codes and LDPC codes, because their error rate performance approaches asymptotically the Shannon limit. Much research is devoted to characterizing the performance of LDPC codes and designing codes that have good performance. Commonly, a graph, the Tanner graph, is associated with the code and an important parameter affecting the performance of the code is the girth of its Tanner graph. In our work, we consider the design of structured regular LDPC codes whose Tanner graphs have large girth. The regularity and structure of LDPC codes utilize memory more efficiently and simplify the implementation of LDPC coders. The Tanner graph is a special type of graph, a bipartite graph, where the nodes divide into two disjoint classes with edges only between nodes in the two different classes. The problem we have been considering is a generic problem in graph theory, namely, that of designing bipartite graphs with large girth. We actually have studied a more special class of this generic problem, in particular, the design of undirected regular bipartite graphs with large girth. Learn more.**Image and Video Processing**

### Content-based Image Sequence Representation

We explore three-dimensional video representations, modeling human motion, generative video, video over wireless, and predictive lossy compression. Learn more.