Many natural and man-made signals can be well modeled as having a few degrees of freedom relative to their "size"/"dimension", due to natural parameterizations or constraints; examples range from the classical band-limited signals that have been studied for many decades, to collections of video and acoustic signals observed from multiple viewpoints and locations in a network-of-sensors and to internet "signals" generated with limited network connectivity. The inherent low-dimensional structure of such signals may be mathematically modeled via combinatorial and/or geometric concepts, such as sparsity, unions-of-subspaces, manifolds, or mixtures of factor analyzers, and are revolutionizing the way we address inverse problems (e.g., signal recovery, parameter estimation, or structure learning) from dimensionality-reduced or incomplete data.

Addressing inverse problems by using a low dimensional model (LDM) to arbitrate the solution among infinitely many possible candidates for the unknown signal (i.e., as a prior, in Bayesian terms) typically leads to optimization problems with exponential complexity. Surprisingly, convex relaxations of specific LDM (priors) produce solutions that are provably close to (or even exactly the same as) an exhaustive search result, at the cost of a slight penalty in the number of required observations. For example, theoretically, using the 1-norm or the nuclear-norm is analogous to seeking the sparsest solution in compressive sensing (CS) or finding the minimum rank solution in matrix completion (MC), respectively, both known to be NP-hard problems. Unfortunately, many other interesting LDMs are intrinsically combinatorial and cannot be "convexified" (or can only be approximated up to constant factors). Such problems require explicitly combinatorial approximation algorithms that can go beyond simple LDM selection heuristics towards provable solution quality as well as runtime/space bounds.

We live in an era of large networks generating lots of data whose topologies are important but are only partially known to us. Detection of communities in such networks involves hypothesis testing on nodes and edges. In many networks, edges reflect the existence of significant pairwise correlation or partial correlation between data generated at the nodes. When the thresholded sample correlation is used to construct the network this problem is called correlation mining. For small sample size and large number of nodes there may be many false positives that prevent accurate discovery of topology and community structure. This talk will review the correlation mining problem and present applications in genomics, computational neuroscience, and the analysis of financial time series.

This talk will review our recent work on the application of the alternating direction method of multipliers (ADMM) to several imaging inverse problems. We will show how ADMM provides an
efficient and modular optimization tool, which allows addressing a wide variety of problems (namely, image restoration and reconstruction, under Gaussian, Poissonian, or multiplicative
noise) using several different types of regularizers (such as total variation, frame-based analysis, frame-based synthesis, or hybrid/balanced analysis-synthesis regularization), and
formulations (constrained or unconstrained optimization). We will describe very recent work on the use of ADMM for blind deconvolution and in dealing efficiently with non-periodic boundary
conditions. Finally (time permitting), we will also show how ADMM can be used to efficiently perform maximum a posteriori inference in probabilistic graphical models.

I will discuss several problems in radar and array imaging in which ideas from convex optimization have proven to be surprisingly efficient. In the first part of my talk I will analyze theoretically and numerically the performance of sparsity-exploiting algorithms for the detection of targets in the azimuth-range domain and in the azimuth-range-Doppler domain using MIMO radar. We consider two approaches that both combine some form of randomization with tools from compressive sensing. I will discuss benefits and limitations of the proposed methods, as well as some open problems. In the second part of my talk I will report on recent progress in array imaging when intensity-only measurements (the phase information is completely absent) are available. In particular, we will see that for certain types of random measurements an image can be recovered exactly from its intensity-only measurements by solving a convenient semidefinite program. Potential applications of this methodology, known as PhaseLift, in Terahertz imaging will be presented.

For more than 20 years, decompositions of higher-order tensors have played a key role in research on independent component analysis and blind source separation. Nowadays tensors are intensively studied in many disciplines. They open up remarkable new possibilities in signal processing, array processing, data mining, machine learning, system modelling, scientific computing, statistics, wireless communication, audio and image processing, biomedical applications, bio-informatics,etc. On the other hand, tensor methods have firm roots in multilinear algebra, algebraic geometry, numerical mathematics and optimization.

We give a brief introduction to the subject and discuss new trends and perspectives. We pay special attention to new developments relevant for multi-sensor processing, in particular in signal separation. We also pay attention to the current progress in numerical multilinear algebra.

Communication systems via satellite provide an unprecedented coverage at low cost. However, satellite networks as a means of content delivery are meeting increased competition from terrestrial communication systems. To stay competitive, innovative, cost efficient and scalable satellite services providing multimedia delivery, mobile communication services, public safety communications, backhaul etc. must be developed. The efficient and reliable delivery of these services poses several technical challenges. We discuss how signal processing techniques can be used to address some of these challenges, including diversity techniques, advanced multi-channel transmission and reception schemes, interference mitigation, and cognitive satellite communications.

A defining feature of a smart grid is its ability to adapt to changing operating conditions and contingencies by leveraging advanced sensing, communication, and networking capabilities. However, relying networking for grid monitoring and real time operation comes with increasing security risks of cyber-attacks.

In this talk, we consider cyber attacks on a power grid where an adversary manipulates analog and digital data with the goal of misleading the control center with an incorrect network topology and erroneous operating state. We present a number of attack mechanisms and counter measures.