Comparative analysis of compressive sensing approaches for recovery of missing samples in implantable wireless Doppler device

An implantable wireless Doppler device used in microsurgical free flap surgeries can suffer from lost data points. To recover the lost samples, the authors considered the approaches based on a recently proposed compressive sensing. In this paper, they performed a comparative analysis of several different approaches by using synthetic and real signals obtained during blood flow monitoring in four pigs. They considered three different bases functions: Fourier bases, discrete prolate spheroidal sequences and modulated discrete prolate spheroidal sequences, respectively. To avoid the computational burden, they considered the approaches based on the l₁ minimisation for all the three bases. To understand the trade-off between the computational complexity and the accuracy, they also used a recovery process based on a matching pursuit and modulated discrete prolate spheroidal sequences bases. For both the synthetic and the real signals, the matching approach with modulated discrete prolate spheroidal sequences provided the most accurate results. Future studies should focus on the optimisation of the modulated discrete prolate spheroidal sequences in order to further decrease the computational complexity and increase the accuracy.