Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 102581, 27 pages
doi:10.1155/2010/102581
Research Article

Blind Deconvolution of the Aortic Pressure Waveform Using the Malliavin Calculus

Ahmed S. Abutaleb,1,2 M. El-Sayed Waheed,3 and Nermeen M. Elhamy3

1Lincoln Laboratory, MIT, Lexington, MA, USA
2Department of Biomedical Engineering and Systems, Faculty of Engineering, Cairo University, Giza, Egypt
3Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

Received 18 June 2010; Accepted 18 July 2010

Academic Editor: Ming Li

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.

Abstract

Multichannel Blind Deconvolution (MBD) is a powerful tool particularly for the identification and estimation of dynamical systems in which a sensor, for measuring the input, is difficult to place. This paper presents an MBD method, based on the Malliavin calculus MC (stochastic calculus of variations). The arterial network is modeled as a Finite Impulse Response (FIR) filter with unknown coefficients. The source signal central arterial pressure CAP is also unknown. Assuming that many coefficients of the FIR filter 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 proposed Malliavin calculus-based method. We have been able to deconvolve the measurements and obtain both the source signal and the arterial path or filter. The presented examples prove the superiority of the proposed method, as compared to conventional methods.