Deep Null Space Learning Improves Dataset Recovery for High Frame Rate Synthetic Transmit Aperture Imaging

Synthetic transmit aperture (STA) imaging benefits from the two-way dynamic focusing to achieve optimal lateral resolution and contrast resolution in the full field of view, at the cost of low frame rate (FR) and low signal-to-noise ratio (SNR). In our previous studies, compressed sensing-based STA (CS-STA) and minimal ${l}_{{2}}$ -norm least squares (LS-STA) methods were proposed to recover the complete STA dataset from fewer Hadamard-encoded (HE) plane wave (PW) transmissions. Results demonstrated that, compared with STA imaging, CS/LS-STA can maintain the high resolution of STA in the full field of view and improve the contrast in the deep region with increased FR. However, these methods would introduce errors to the recovered STA datasets and subsequently produce severe artifacts to the beamformed images, especially in the shallow region. Recently, we discovered that the theoretical explanation for the error introduced in the LS-STA-based recovery is that the LS-STA method neglects the null space component of the real STA dataset. To deal with this problem, we propose to train a convolutional neural network under the null space learning framework (CNN-Null) to estimate the missing null space component) for high-accuracy recovery of the STA dataset from fewer HE PW transmissions. The mapping between the low-quality STA dataset (i.e., the range space component of the real STA dataset recovered using the LS-STA method) and the missing null space component of the real STA dataset was learned by the network with the high-quality STA dataset (obtained using full HE STA (HE-STA) imaging) as training labels. The performance of the proposed CNN-Null method was compared with the baseline LS-STA, conventional STA, and HE-STA methods, in terms of the visual quality, the normalized root mean square error (NRMSE), the generalized contrast-to-noise ratio (gCNR), and the lateral full-width at half-maximum (FWHM). The results demonstrate that the proposed method can greatly improve the recovery accuracy of the STA datasets (lower NRMSE) and, therefore, effectively suppress the artifacts presented in the images (especially in the shallow region) obtained using the LS-STA method (with a gCNR improvement of 0.4 in the cross-sectional carotid artery images). In addition, the proposed method can maintain the high lateral resolution of STA with fewer (as low as 16) PW transmissions, as LS-STA does.

I. Introduction

Thanks to the two-way dynamic focusing, when combined with the same beamforming method, synthetic transmit aperture (STA) imaging can achieve comparatively high spatial (lateral) resolution and contrast resolution among all the imaging sequences [1]. In STA imaging, all the transducer elements are activated individually and sequentially to transmit spherical waves and to obtain low-quality images. Thereafter, transmit focusing can be resynthesized at all image points by coherently summing these images to obtain the final high-resolution STA image. However, owing to the limited energy transmitted by the individual element in each transmission, STA imaging severely suffers from the low signal-to-noise ratio (SNR) issue (especially in the deep region). In addition, as STA imaging requires activating all the elements sequentially, its frame rate (FR) is limited by a large number of transmissions. Fig. 1.

Illustration of the range-null space decomposition.