%0 Journal Article
%T Blind Deconvolution of the Aortic Pressure Waveform Using the Malliavin Calculus
%A Ahmed S. Abutaleb
%A M. El-Sayed Waheed
%A Nermeen M. Elhamy
%J Mathematical Problems in Engineering
%D 2010
%I Hindawi Publishing Corporation
%R 10.1155/2010/102581
%X 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. 1. Introduction In this paper, we present a new approach to monitor central arterial pressure using the Multichannel Blind Deconvolution (MBD) [1, 2]. A multichannel blind deconvolution problem can be considered as natural extension or generalization of instantaneous Blind Source Separation (BSS) problem [3, 4]. The problem of BSS has received wide attention in various fields such as signal analysis and processing of speech, image [5, 6], and biomedical signals, especially, signal extraction, enhancement, denoising, model reduction, and classification problems [7¨C9]. The MBD is the technique that allows the estimation of both an unknown input and unknown channel dynamics from only channel outputs. Although one cannot place a sensor [10] to directly measure the input, yet, it may be recovered from the outputs that are simultaneously measured at the multiple branches of the system. The MBD technique distinguishes itself from other techniques that apply a predetermined transfer function [11, 12] to interpret sensor data. The other techniques cannot account for individual differences nor can they account for dynamic changes in the subject¡¯s physiologic state. The physiologic state of the cardiovascular (CV) system can be most accurately assessed by using the aortic blood pressure or CAP [7, 13, 14] and flow. However, standard measurement of these signals, such as catheter, entails costly and risky surgical procedures. Therefore, most of the practically applicable methods aim to monitor the CV system based on peripheral circulatory signals, for example, arterial blood pressure at a distant
%U http://www.hindawi.com/journals/mpe/2010/102581/