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Mathematical Problems in Engineering
Volume 2010, Article ID 602373, 21 pages
Research Article

Multichannel Blind Deconvolution Using the Stochastic Calculus for the Estimation of the Central Arterial Pressure

1MIT/Lincoln Laboratory, Lexington, MA, USA
2Systems and Bioengineering Departments, School of Engineering, Cairo University, Giza, Egypt
3Mathematics Departments, School of Science, Zagazig University, Zagazig, Egypt

Received 11 December 2009; Revised 1 May 2010; Accepted 17 May 2010

Academic Editor: Jerzy Warminski

Copyright © 2010 Ahmed S. Abutaleb et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new tool for estimation of both the central arterial pressure and the unknown channel dynamics has been developed. Given two peripheral waveform measurements, this new signal processing algorithm generates two models that represent the distinct branch dynamic behavior associated with the measured signals. The framework for this methodology is based on a Multichannel Blind Deconvolution (MBD) technique that has been reformulated to use Stochastic Calculus (SC). The technique is based on MBD of dynamic system are mathematically analyzed, in order to reconstruct the common unobserved input within an arbitrary scale factor. The convolution process is modeled as a Finite Impulse Response (FIR) filter with unknown coefficients. The source signal is also unknown. Assuming that one of the FIR filter coefficients are time varying, we have been able to get accurate estimation results for the source signal, even though the filter order is unknown. The time varying filter coefficients have been estimated through the SC algorithm, and we have been able to deconvolve the measurements and obtain both the source signal and the convolution path. The positive results demonstrate that the SC approach is superior to conventional methods.