Monday, September 7th 2015
Title: Compressive Sensing and Robust Signal Processing
Compressive sensing is an area that has been intensively developed in the last few years. It deals with sparse randomly undersampled signals and offers a new sensing modality as an alternative to the traditional sampling theory. Hence, the main idea behind the compressive sensing is to reduce the sampling rate below the one defined by the Nyquist-Shannon sampling theorem and then to reconstruct the entire information from reduced observations. Consequently, the compressive sensing enables signal compression in the initial phase of sampling. The powerful reconstruction algorithms provide that significant number of missing samples can be recovered, under the assumption that the sparsity property is satisfied. Sparsity means that in certain domain the signal can be represented by a small number of important non-zero coefficients, while the remaining ones are either zero or negligible. In terms of resources, the compressive sensing approach is far less demanding and requires fewer sensors for signal sampling. As such, the compressive sensing becomes very attractive not only as a research topic, but also in many different applications dealing with a huge number of measurements, as it is the case with biomedical, radar, multimedia applications etc.
This presentation is structured as follows. At the beginning, an introduction to the compressive sensing is presented. The main constrains are discussed, such as: Signal sparsity, Restricted Isometry Property and Incoherence. Then the standard and advanced algorithms for compressive sensing signal reconstruction are analyzed. They belong to the classes of basis pursuit and Iterative thresholding algorithms. An advanced single iteration threshold based algorithm is presented. Also, a combination of compressive sensing and L-estimation theory is considered in order to provide an ideal filtering of signals affected by heavy-tailed noise. Following the robust statistics theory, it is possible to use generalized deviations instead of the Fourier transform of signal with missing samples, leading to an efficient reconstruction algorithm explained in this presentation. It enables to choose an appropriate norm for various types of noise. Next, the gradient-based algorithm dealing with almost sparse signals is analyzed. Finally, a short overview about the signal reconstruction in the Hermite transform domain, together with some relation between compressive sensing and time-frequency analysis is given.
Colloquium coordinators are Prof.dr. M. Aiello (e-mail :
Prof.dr. M. Biehl (e-mail:
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