Partial Hadamard encoded synthetic transmit aperture for high frame rate imaging with minimal l ₂-norm least squares method

Abstract

Objective: 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 transducer element must be activated individually. In our previous study, we encoded all the transducer 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 (~ hours). In this study, we propose to accelerate the complete STA dataset reconstruction with minimal l2-norm least squares method. Approach: Partial Hadamard apodized PW transmissions were performed to acquire the PW dataset. Thereafter, the complete STA dataset can be reconstructed from the PW dataset with minimal l2-norm least squares method. Due to the orthogonality of partial Hadamard matrix, the minimal l2-norm least squares solution can be easily calculated. Main results: The proposed method is tested with simulation data and experimental phantom and in-vivo data. The results demonstrate that the proposed method achieves ~5×103 times faster reconstruction speed than CS algorithm. The simulation results demonstrate that the proposed method is capable of achieving the same accuracy as the conventional CS-STA method for the STA dataset reconstruction. 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. Significance: In conclusion, the improved image quality and reduced computational time of LS-STA pave the way for its real-time applications in the clinics.