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.
An approach to multi-channel blind de-convolution is developed, which uses an adaptive filter that performs blind source separation in the Fourier space. The approach keeps (during the learning process) the same permutation and provides appropriate scaling of components for all frequency bins in the frequency space. Experiments indicate that Generalized Laplace Distribution can be used effectively to blind de-convolution of convolution mixtures of sources in Fourier space compared to the conventional Laplacian and Gaussian function.
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.
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