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

Abstract

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.

Observer-Based Deconvolution of Deterministic Input in Coprime Multichannel Systems With Its Application to Noninvasive Central Blood Pressure Monitoring

“…The methodology, when applied to coprime multichannel systems with unknown input signal, determines the channel dynamics and then deconvolves the input signal by exploiting the correlation relationship between the channels. In particular, the input-deconvolution step of the methodology has employed various techniques, such as direct inverse filtering (IF) [7,20], least-squares and maximum-likelihood-type deconvolution [21,22], and the design of dedicated deconvolution filters [23,24]. Direct inverse filtering has been a straightforward choice due to the nonminimum phase nature of the channel dynamics associated with the BP wave propagation in the arteries [25].…”

“…The leastsquares and maximum likelihood-type deconvolution techniques were developed primarily for finite impulse response channel dynamics [26,27]. Hence, central aortic BP deconvolution based on these techniques involved the finite impulse response filter approximation of the BP propagation channel dynamics [21,22]. To relax such restrictions, design methodologies for the input deconvolution filters applicable to coprime multichannel systems with infinite impulse response channel dynamics have been developed [23,24,28].…”