# Biomedical signals

The acquisition and processing of bioelectrical signals that appear in the human body is a common theme in clinical studies for evaluating the health status of a patient. The electrical activity of cells and tissue can be recorded from different organs. Examples of bioelectrical recordings are the electrocardiogram (ECG), the electroencephalogram (EEG), the electrolaryngram (ELG), the electromyogram (EMG) and the electro-oculogram (EOG), which measure respectively the electrical activity in the heart, brain, larynx, muscles and eyes.

The current medical monitoring devices become smaller and wireless and hence demand ever more sophisticated techniques to acquire and process data. Our new sampling and reconstruction technique reduces the amount of data to be stored or transmitted because it allows to reconstruct the biomedical signals from far less measurements than usual. The samples are collected at a fraction $1/r$ of the Nyquist rate M (in Hertz), hence achieving a compression rate of $(100/r)$ %.

We show the reconstruction of an 8 second [1-20] Hz bandpass filtered EEG signal and a 30 second unfiltered EEG signal, both from only 11.1% of the original dataset which was collected at 256 Hz. The cross-correlation of both compact sparse representations is around 98%.

Likewise, biomedical scanners can be made faster because the amount of data that needs to be collected to reconstruct an image can be hugely reduced. Considering the fact that the image is almost certainly compressible, one can immediately reduce the number of measurements. And the fact that the measurements are not collected in a random way in the new technique, guarantees that the reconstruction is entirely predictable. Also the image reconstruction time is much more reasonable because of the low complexity of the new technique.