Compressive sensing (CS) has recently emerged as an important area of research in image sensing and processing. Conventional sensing systems employ a two-step procedure: i) data acquisition; and ii) data compression for subsequent storage or communication. CS systems, in contrast, acquire the data directly in a compressed format. CS signal acquisition or measurement involves projecting the underlying signal or image onto a set of vectors and CS recovery involves solving an inverse problem.
There are two hallmarks of the original CS theory. First, the projection vectors are typically constituted uniformly at random. Second, the inverse recovery problem is regularized based on the assumption that the underlying signal or image admits a sparse representation in some orthonormal basis or frame. However, it has been recognized, even in some of the early CS studies, that improved recovery performance could be achieved by using optimized projection vectors in lieu of the random ones; further, it has also been recently recognized that improved recovery performance could also be achieved by leveraging a signal model that goes beyond the conventional -- often overly primitive -- sparse one.
This talk outlines how to build upon recent advances in the fields of information theory and communications to design CS projections -- or measurement kernels -- matched to a general signal statistical model. The crux of the design approach is the realization that the projections design problem for CS systems exhibits parallels with the precoder design problem for multiple-input-multiple-output (MIMO) communications systems: in the communications problem a source is being matched to a channel whereas in the CS problem a channel, or equivalently the noise covariance, is being matched to the source. This new design approach is shown to lead to theoretical results, which unveil key operations effected by the projection designs, as well as state-of-the-art experimental results in practical CS imaging problems.
This represents joint work with William Carson (U. Porto, Portugal), Minhua Chen (Duke U., USA), Lawrence Carin (Duke U., USA) and Robert Calderbank (Duke U., USA).
Miguel Rodrigues is a Senior Lecturer with the Department of Electronic and Electrical Engineering, University College London, UK. He was previously with the Department of Computer Science, University of Porto, Portugal, raising through the ranks from Assistant to Associate Professor, where he also led the Information Theory and Communications Research Group at Instituto de Telecomunicações - Porto.
He received the Licenciatura degree in Electrical Engineering from the University of Porto, Portugal in 1998 and the Ph.D. degree in Electronic and Electrical Engineering from University College London, UK in 2002. He has carried out postdoctoral research work both at Cambridge University, UK, as well as Princeton University, USA, in the period 2003 to 2007. He has also held visiting research appointments at Princeton University, USA and Duke University, USA in the period 2007 to 2012. He is also a Visiting Fellow at Cambridge University.
His research work, which lies in the general areas of information theory, communications and signal processing, has led to nearly 100 papers in journals and conferences to date.
Dr. Rodrigues was honored with the IEEE Information Theory and Communications Societies Joint Paper Award 2011 for his work on ``Wireless Information-Theoretic Security'' (jointly with M. Bloch, J. Barros and S. McLaughlin). Dr. Rodrigues was also the recipient of the Prize Engenheiro António de Almeida, the Prize Engenheiro Cristiano Spratley, and the Merit Scholarship from the University of Porto.