This is a multi-sensor application, where 12 ECG waveforms (12-lead ECG) are received from the patient (Fig. a) and then sampled simultaneously at common time instances (Fig. b). The streaming ECG signals, are measured in the online fashion shown in (Fig. c), for one signal only for brevity.

Particularly, the projection vectors 2 are multiplied (inner product) with intervals from each ECG signal in a sliding and overlapping manner. The number of measurements depends on the time lag, k, between two successive signal intervals. This process results in vectors yi, with 12 measurements each (one per signal), which are transmitted. Their noisy counterparts, ¯yi reach the receiver-end (Fig. d) and they are used for the recovery of the 12 ECG signals, in real-time, based on the online MMV approach developed in objective 3. ECG

At both ends of the wireless link there are battery powered devices and the ultimate goal is to consume as less energy as possible in all of the aforementioned processing stages. This can be translated as follows: a) compute the measurements with as less operations as possible, b) transmit as less measurements as possible, and c) recover the signals with very low complexity.

Echo cancellation, which is a key ingredient towards high-quality communications, appears to be a very challenging filtering task due to a number of inherent peculiarities. In an ideal communication setting, the loudspeaker at the far-end would either exclusively transmit the voice of the person at the near-end or nothing if this person is silent. This should be the case irrespective of whether the person at the far-end is speaking or not. However, in realistic conditions, this is not true; the far-end speech signal travels through the communication channel and it is transmitted via the loudspeaker in the near-end room.

Due to the room impulse response and delays in the communication line, the microphone at the near-end captures a filtered version of the far-end speech, which is transmitted back to the far-end in the form of annoying echo. In wired communications, even when a room is not involved in echo generation, known as acoustic echo, electrically induced echo appears due to unbalanced coupling between the 2-wire and 4-wire circuits. The echo cancellation task aims at estimating the impulse response corresponding to the echo path. Doing so, the echo can be reproduced at the far-end and be subtracted from the received signal. In this way, the received signal is cleansed from the echo before its transmission through the loudspeaker. All modern communication systems carries in one way or the other types of echo cancellers. Advances in this topic are important for future immersive communications.

In SOL project, the fact that the room impulse response is sparse was exploited. Moreover, the problem is inherently online and time-varying rendering it suitable for the techniques developed in SOL project.

Functional Magnetic Resonance Imaging (fMRI) is a powerful non-invasive tool for localizing and analyzing brain activity. Most commonly it is based on blood oxygenation level-dependent (BOLD) contrast, which allows the detection of local changes in the hemodynamic flow of oxygenated blood in activated brain areas.

In the brain, tasks involving action, perception, cognition, etc., are performed via the simultaneous activation of a number of functional brain networks, which are engaged in proper interactions in order to effectively execute the task. Such networks are usually related to low-level brain functions and they are defined as a number of \textit{segregated} specialized small brain regions, potentially distributed over the whole brain. These regions collaborate in order to coherently perform a certain brain function.

The observed signal results from the mixture of all the activated brain networks. In order to better understand the way that brain operates, it is important to unmix these activations and specify the exact regions corresponding to each network taking into account that such regions might also overlab. This is a quite hard blind source separation task and several approaches have been proposed for this reason. Lately, the sparse structure of the spatial maps have been exploited in order to perform such an unmixing via a properly constrained matrix factorization task. In SOL, a similar approach based on dictionary learning was followed, which was also rendered computationally efficient via a properly defined randomized dimensionality reduction scheme.