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

Abstract

Synthetic transmit aperture (STA) can achieve very high spatial resolution thanks to its dynamic focusing in both transmit and receive. However, because each element is activated individually and sequentially to transmit a spherical wave, the imaging frame rate is low. In addition, the low transmitted energy leads to low signal-to-noise ratio (SNR) echoes. In our previous study, we proposed to use compressed sensing (CS) algorithm to recover full STA dataset from fewer apodized plane wave (PW) transmissions (CS-STA). In this way, the frame rate and SNR of STA imaging can be significantly improved. However, owing to the iterative nature of CS algorithms, the reconstruction of STA dataset is very time consuming, which hampers its real application. In this study, the minimal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l$</tex> <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -norm least square method is used to recover the STA dataset with significantly reduced computational time. Simulation shows that the proposed method can achieve ~5×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> times acceleration for STA dataset reconstruction, compared with CS-STA. Simulated B-mode images show that the proposed method is capable of achieving higher generalized contrast-to-noise ratios (gCNRs) for anechoic inclusions than STA, with maintained spatial resolution. Simulated strain images show that the proposed method could preserve the phase information of radio-frequency data during the reconstruction, and achieve acceptable quality in strain estimation in noise-free condition.