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An extended least squares method for robust, angle-independent 2-D vector velocity estimation using plane-wave ultrasound imaging is presented. The method utilizes a combination of least squares regression of Doppler autocorrelation estimates and block matching to obtain aliasing-resistant vector velocity estimates. It is shown that the aliasing resistance of the technique may be predicted using a single parameter, which is dependent on the selected transmit and receive steering angles. This parameter can therefore be used to design the aliasing-resistant transmit–receive setups. Furthermore, it is demonstrated that careful design of the transmit–receive steering pattern is more effective than increasing the number of Doppler measurements to obtain robust vector velocity estimates, especially in the presence of higher order aliasing. The accuracy and robustness of the method are investigated using the realistic simulations of blood flow in the carotid artery bifurcation, with velocities up to five times the Nyquist limit. Normalized root-mean-square (rms) errors are used to assess the performance of the technique. At −5 dB channel data blood SNR, rms errors in the vertical and horizontal velocity components were approximately 5% and 15% of the maximum absolute velocity, respectively. Finally, the in vivo feasibility of the technique is shown by imaging the carotid arteries of healthy volunteers. [ABSTRACT FROM AUTHOR]

A Gaussian integer is a complex number whose real and imaginary parts are both integers. Meanwhile, a sequence is defined as perfect if and only if the out-of-phase value of the periodic autocorrelation function is equal to zero. This paper presents two novel classes of perfect sequences constructed using two groups of base sequences. The nonzero elements of these base sequences belong to the set \\ ± 1,\ ± j\. A perfect sequence can be obtained by linearly combining these base sequences or their cyclic shift equivalents with arbitrary nonzero complex coefficients of equal magnitudes. In general, the elements of the constructed sequences are not Gaussian integers. However, if the complex coefficients are Gaussian integers, then the resulting perfect sequences will be Gaussian integer perfect sequences (GIPSs). In addition, a periodic cross-correlation function is derived, which has the same mathematical expression as the investigated sequences. Finally, the maximal energy efficiency of the proposed GIPSs is investigated. [ABSTRACT FROM PUBLISHER]