Partial Hadamard Encoded Synthetic Transmit Aperture for High Frame Rate Imaging with Minimal l2-Norm Least Square Method

Synthetic transmit aperture (STA) ultrasound imaging is well known for ideal focusing in the full field of view. However, it suffers from low signal-to-noise ratio (SNR) and low frame rate, because each array element must be activated individually. In our previous study, we encoded all the array elements with partial Hadamard matrix and reconstructed the complete STA dataset with compressed sensing (CS) algorithm (CS-STA). As all the elements are activated in each transmission and the number of transmissions is smaller than that of STA, this method can achieve higher SNR and higher frame rate. Its main drawback is the time-consuming CS reconstruction. In this study, we accelerate the complete STA dataset reconstruction with minimal l2-norm least square method. Thanks of the orthogonality of partial Hadamard matrix, the minimal l2-norm least square solution can be easily calculated. The proposed method is tested with simulation data and experimental phantom and in-vivo data. The results demonstrate that the proposed method achieves ~5*10^3 times faster reconstruction speed than CS algorithm. The simulation results demonstrate that the proposed method is capable of achieving the same accuracy for STA dataset reconstruction as conventional CS-STA method. The simulations, phantom and in-vivo experiments show that the proposed method is capable of improving the generalized contrast-to-noise ratio (gCNR) and SNR with maintained spatial resolution and fewer transmissions, compared with STA. In conclusion, the improved image quality and reduced computational time of LS-STA pave the way for its real-time applications in the clinics.