3-D biquaternionic analytic signal and application to envelope detection in 3-D ultrasound imaging

This paper gives an algebraic framework for 3-D analytic signals and realizes a numerical implementation of Clifford Fourier transformation and Clifford biquaternions. By applying the hypercomplex analytic signal, the module and partial modules of a biquaternion are proposed. Our method is applied to the ultrasound data from a phantom with a biopsy needle inserted. The biquaternion pseudo-envelope of a radio frequency ultrasound volume data is introduced from the partial module of the ultrasound volume biquaternionic analytic signal. This method shows several advantages comparing with the 1-D envelope results. When the envelope of a radio frequency ultrasound volume is calculated based on conventional 1-D method, there are possible losses of information as we expected. As the result of that, the biquaternion pseudo-envelope detection method is preferred in order to take into account the information of the other dimensions of data and to obtain a better visual appearance of the needle.