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Signal/Image Reconstruction from Sparse Measurements: Theory, Algorithms and Applications

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Signal Processing Laboratory Seminar

Consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomial or piecewise sinusoidal signals, and call the number of degrees of freedom per unit of time the rate of innovation. Classical sampling theory does not enable a perfect reconstruction of such signals since they are not bandlimited. In this talk, we show that many signals with finite rate of innovation can be sampled and perfectly reconstructed using a rich variety of sampling kernels and fast reconstruction algorithms. The class of kernels that can be used includes functions satisfying Strang-Fix conditions, Exponential Splines, functions with rational Fourier transform and the sinc or Gaussian functions.

Retrieval of such signals in noise is also considered. Lower bounds by Cramer-Rao are given, and an iterative algorithm due to Cadzow is shown to perform close to optimal over a wide range of signal to noise ratios. This indicates the robustness of the proposed methodologies.

Finally, applications of such methods to image super-resolution and distributed video compression are presented.


Pier Luigi Dragotti is currently a Senior Lecturer (Associate Professor) in the Electrical and Electronic Engineering Department at Imperial College, London. He received the Laurea Degree (summa cum laude) in Electrical Engineering from the University Federico II, Naples, Italy, in 1997; the Master degree in Communications Systems from the Swiss Federal Institute of Technology of Lausanne (EPFL), Switzerland in 1998; and PhD degree from EPFL , Switzerland, in April 2002 (thesis adviser Prof. M. Vetterli). In 1996, he was a visiting student at Stanford University, Stanford, CA, and, from July to October 2000, he was a summer researcher in the Mathematics of Communications Department at Bell Labs, Lucent Technologies, Murray Hill, NJ. Before joining Imperial College in November 2002, he was a senior researcher at EPFL working on distributed signal processing for sensor networks for the Swiss National Competence Center in Research on Mobile Information and Communication Systems. Dr Dragotti is the co-organizer of the following special sessions: ‘Image Compression beyond Wavelets’ at the Visual Communications and Image Processing conference (VCIP 2003), ‘Sensing Reality and Communicating Bits’ at the IEEE International Conference of Acoustic, Speech and Signal Processing (ICASSP 2006), ‘Signal/Image Reconstruction from Sparse Measurements’ at the IEEE International Conference on Image Processing (ICIP 2006) and ‘Sparsity and Sampling’ at the SPIE Conference on Wavelet Applications in Signal and Image Processing, Wavelets XII . Since August 2006, Dr Dragotti has been an associate editor of the IEEE Transactions on Image Processing.

This talk is part of the Signal Processing and Communications Lab Seminars series.

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