Subspace-Based Blood Power Spectral Capon Combined with Wiener Postfilter to Provide a High-Quality Velocity Waveform with Low Mathematical Complexity

Abstract

In Doppler analysis, the power spectral density (PSD), which accounts for the axial velocity distribution of the blood scatterers, is estimated. The conventional spectral estimator is Welch's method, which suffers from frequency leakage at small observation window length. The performance of adaptive techniques such as blood power Capon (BPC) has been promising at the cost of higher computation complexity. Reducing the computational complexity while retaining the benefits of BPC would be necessary for real-time implementation. The purpose of the work described here was to investigate whether it is possible to decrease the computation load in BPC and still obtain acceptable results. The computation complexity in BPC is owing primarily to the matrix inversion required for computing the PSD estimate. We here propose the subspace blood power Capon technique, which employs a data covariance matrix with reduced number of rows in estimation of the weight vector. In maximum velocity estimation in the spectra, the signal noise slope intersection envelop estimator that makes use of the integrated power spectrum is employed. The evaluations are made based on both simulated and in vivo data. The results indicate that it is possible to reduce the order of complexity to almost 12.25% at the cost of 2.31% and 2.24% increases in the relative standard deviation and relative bias of the estimates. Moreover, the Wiener post-filter as a post-weighting factor, which will be multiplied by the final weight vector of the spectral estimator, estimates the power of the desired signal and the power of the interference plus noise to improve the contrast. The proposed estimator has exhibited a promising performance at beam-to-flow angles of 45°, 60° and 75°. Furthermore, the robust performance of the proposed estimator against variation in the flow rate is also documented.