Blind Deconvolution of the Aortic Pressure Waveform Using the Malliavin Calculus

Ahmed S Abutaleb,M El-Sayed Waheed,Nermeen M Elhamy

doi:10.1155/2010/102581

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.

Highlights

We present a new approach to monitor central arterial pressure using the Multichannel Blind Deconvolution MBD 1, 2
If we make only one of the FIR filter parameters changing over time, the problem is handled by the Ito calculus 27, while, if we make more than one of the FIR filter parameters changing over time, the problem could be handled by the Malliavin calculus as we propose in this paper
An absolute central aortic pressure waveform is determined by scaling the estimated input based on the measured waveforms

Summary

Introduction

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 MBD is the technique that allows the estimation of both an unknown input and unknown channel dynamics from only channel outputs. 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 other techniques cannot account for individual differences nor can they account for dynamic changes in the subject’s physiologic state

Methods

Discussion

Conclusion