Compressive Sensing system for recording of ECoG signals in-vivo

each channel must have a shared or dedicated module to process, compress and digitalize thesignal and a transmitter module in order to send out of the scalp the registered information.2.3. Data Compression Methods [18]The traditional approach of signal reconstruction is based on the Shannon-Nyquist samplingtheorem which states that the sampling rate must be twice the highest frequency of the signal.Similarly, the fundamental theorem of linear algebra expresses that the number ofmeasurements should be at least as large as its length in order to ensure a correctreconstruction. The aim of compression methods is to come through these limitations byapplying a reversible reduction to the signal to be transmitted. The empirical observation thatmany types of signals of images can be well-approximated by a sparse expansion in terms of asuitable basis, that is, by only a small, number of non-zero coefficients is the key of many lossycompression techniques such a JPEG or MP3. The compression is carried out by storing thelargest basis coefficients and setting the others to zero, and it is a good technique when fullinformation of the signal is available. However, when the sensing procedure is costly, one mightask about the chance about directly obtaining the compressed version by taking a small amountof linear and non-adaptive measurements. CS technique responds to this compressionapproach, which roughly sketched in Fig. 2.3.1 by considering compression is accomplished inthe input signal x, from N samples to K measurements, being N >> K.Figure 2.3.1. Transmission and Reception schemes in CS.In the last ten years, CS applications have become more and more relevant in the area of signalacquisition and imaging compression. In 2008 Boufounos and Baraniuk have proposed 1-Bit CSmeasurements in order to preserve the sign of the recorded signal [19]. In 2009 Duarte andBaraniuk introduced a variation of CS called Kronecker Compressive Sensing (KCS), whichexploits Kronecker matrix to jointly model as sparsifying basis of multidimensional signals [20].In 2010, an imager/compressor based on real-time in-pixel CS has been developed in the ÉcolePolytechnique Fédérale de Lausanne (EPFL) by applying the concept of Random Convolution[21].32