Deep Neural Oracle with Support Identification in the Compressed Domain

We investigate the advantage of a two-step approach in the recovery of Compressed Sensing (CS) encoded signals in a realistic environment. First, the support of the signal is computed from the compressed measurements exploiting a Deep Neural Network (DNN). Once the support is known, the input signal can be easily recovered by a pseudoinverse operation. We consider a case study involving realistic biomedical signals and a processing architecture based on a limited precision fixed-point arithmetic unit for the implementation of the DNN and the pseudoinverse operation. In this setting, we show that the proposed approach results in a performance improvement of more than 5 dB in terms of average reconstructed signal to noise ratio (ARSNR) compared to CS state-of-the-art approach. This has been possible thanks to two main contributions reported in this paper. The first one is a theoretical investigation of the relationship between the definition of support and both the properties of the input signal and the adopted compression technique. The second one relies on replacing the pseudoinverse operation with a least mean square filter, whose small sensitivity to numerical errors grants advantages in architectures relying on limited precision fixed-point arithmetic units.