A natural replacement for the extensively used Principal Component Analysis (PCA). Uses a generative model containing hidden independent variables (typically nonGaussian iid , though they can also be nonstationary , temporally correlated or a combination of the three). We have developed theoretical and algorithmic advances for convolutional mixing, noisy ICA, and overcomplete ICA (more sources than sensors. This last topic is related to sparse representations (see below). We have particularly concentrated on applications of ICA to Speech and music processing, blind MIMO channel identification, and biomedical signal processing (EEG, ECG). For further details see www.see.ed.ac.uk/~mdavies4/Research/ICA.htm.
Compressed sensing is a new rapidly growing research field emerging primarily in the USA which investigates ways in which we can sample signals at roughly the information rate rather than the Nyquist rate. For example compressed sensing theory has already enabled a 4-fold reduction in acquisition time for MRI images by allowing the under-sampling of k-space (Lustig et al. 2007). It is potentially a very disruptive technology and provides a new way of thinking about how to acquire and code signals in the most efficient manner. Its growing popularity is evident in the forthcoming special issue in IEEE Signal Processing Magazine (Eds: Donoho Baranuik and Vetterli) the large number of research papers (see the Rice University web resource on compressed sensing for example: http://www.dsp.ece.rice.edu/cs) and the growing number of applications that are being explored across a range of disciplines including: Medical imagin Seismic imagin Distributed and remote sensi Analogue to Digital Conversion (DARPA 2005) We are particularly interested in: how the theory can be extended to more sophisticated signal models (beyond sparsity)
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