Binary Compressed Sensing of ECG by Neural Matrix Optimization and Support Oracle

The need of having non-invasive ECG measurements requires the smallest possible wireless sensors, which, on the other hand, suffer from severe hardware resource constraints. These limitations may be addressed with data compression for which one of the most lightweight methods is Compressed Sensing (CS). In CS the encoded signal is the output of a linear operator defined by the so-called sensing matrix. In case this matrix is binary, the encoded signal can be computed as a simple conditioned accumulation of the input samples.To further reduce the size of the encoded signal, frameworks based on Deep Neural Networks (DNNs) have been recently successfully proposed, however, they still struggle with the training of binary encoders. In our work we present a strategy that jointly tailors the binary encoder design problem, and the decoder task, with DNN blocks. The proposed method can either automatically find a suitable density of ones in the sensing matrix, or let one fix a predefined value. The effectiveness of the proposed approach is demonstrated on synthetic ECG signals.