title: Single-ensemble-based eigen-processing methods for color flow imaging--Part II. The matrix pencil estimator.
abstract: Parametric spectral estimators can potentially be used to obtain flow estimates directly from raw slow-time ensembles whose clutter has not been suppressed. We present a new eigen-based parametric flow estimation method called the matrix pencil, whose principles are based on a matrix form under the same name. The presented method models the slow-time signal as a sum of dominant complex sinusoids in the slow-time ensemble, and it computes the principal Doppler frequencies by using a generalized eigen-value problem-formulation and matrix rank reduction principles. Both fixed rank (rank-one, rank-two) and adaptive-rank matrix pencil flow estimators are proposed, and their potential applicability to color flow signal processing is discussed. For the adaptive-rank estimator, the nominal rank was defined as the minimum eigen-structure rank that yields principal frequency estimates with a spread greater than a prescribed bandwidth. In our initial performance evaluation, the fixed-rank matrix pencil estimators were applied to raw color flow data (transmit frequency: 5 MHz; pulse repetition period: 0.175 ms; ensemble size: 14) acquired from a steady flow phantom (70 cm/s at centerline) that was surrounded by rigid-tissue-mimicking material. These fixed-rank estimators produced velocity maps that are well correlated with the theoretical flow profile (correlation coefficient: 0.964 to 0.975). To facilitate further evaluation, the matrix pencil estimators were applied to synthetic slow-time data (transmit frequency: 5 MHz; pulse repetition period: 1.0 ms; ensemble size: 10) modeling flow scenarios without and with tissue motion (up to 1 cm/s). The bias and root-mean-squared error of the estimators were computed as a function of blood-signal-to-noise ratio and blood velocity. The matrix pencil flow estimators showed that they are comparatively less biased than most of the existing frequency-based flow estimators like the lagone autocorrelator.
authors.affiliation: University of Hong Kong, Department of Electrical and Electronic Engineering, Pokfulam, Hong Kong.
authors.forename: Alfred C H
authors.initials: AC
authors.lastname: Yu
authors.forename: Richard S C
authors.initials: RS
authors.lastname: Cobbold
mesh_terms: D000465:Algorithms; D001783:Blood Flow Velocity / Q000502:physiology*; D003326:Coronary Circulation / Q000502:physiology*; D003331:Coronary Vessels / Q000000981:diagnostic imaging*; D018618:Echocardiography, Doppler, Color / Q000295:instrumentation / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted