A comparative analysis of compressive sensing approaches for recovery of missing samples in an implantable wireless Doppler device
February 15, 2014
An implantable wireless Doppler device used in microsurgical free flap surgeries can suffer from lost data points. In order to recover the lost samples, we considered approaches based on recently proposed compressive sensing. In this paper, we carried out a comparative analysis of several different approaches using synthetic signals and real signals obtained during blood flow monitoring in four pigs. We considered three different basis functions: Fourier basis, discrete prolate spheroidal sequences and modulated discrete prolate spheroidal sequences. To avoid the computational burden, we considered approaches based on the $l_1$ minimization for all three bases. To understand the trade-off between the computational complexity and the accuracy, we also used a recovery process based on matching pursuit and modulated discrete prolate spheroidal sequences bases. For both synthetic and real signals, the matching approach with modulated discrete prolate spheroidal sequences provided the most accurate results. Future studies should focus on the optimization of the modulated discrete prolate spheroidal sequences in order to further decrease the computational complexity and increase the accuracy.
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