Clutter rejection filters in color flow imaging: a theoretical approach

Abstract
A general class of linear clutter rejection filters is described, covering the commonly used filter types including FIR/IIR filters with linear initialization, as well as regression filters, where the clutter component is estimated by least square curve fitting. The filter can be described by a complex valued matrix, and a frequency response is defined. However, in contrast to a time invariant filter, the general linear filter may create frequency components which are not present in the input signal. This produces bias in the velocity and velocity spread estimates. It is shown that the clutter filter effect on the autocorrelation estimates can be described by a frequency domain transfer function, but unlike time invariant filters, the transfer function is different for each temporal lag of the autocorrelation function. Using a two dimensional (axial and temporal dimension) model of the received signal, the bias in velocity and velocity spread is quantified, both for the autocorrelation algorithm and the time shift cross-correlation estimator. Theoretical expressions, as well as numerical examples are given.

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