Regularizing the inverse problem of ultrasound beamforming with non-local structure tensor total variation

Researchers are increasingly interested in using inverse problem methodologies for ultrasound image reconstruction instead of conventional beamforming methods, termed the inverse problem of ultrasound beamforming (IPB). This new imaging method promises to increase the frame rate of plane-wave imaging by enabling the reconstruction of high-quality images from fewer plane-wave transmissions compared to conventional beamforming methods. IPB assumes that the RF signals received by the ultrasound probe are linearly related to the beamformed image. In addition to the standard data fidelity term of the inverse problem, a regularization term has to be defined to consider the underlying image's prior information. Its purpose is to alleviate the ill-posed problem and improve the image quality. Herein, the non-local structure tensor total variation is introduced into IPB (IPB-NLSTV) as the regularization term to exploit the image's local structure and non-local self-similarity properties for the reconstructed complex ultrasound image. The performance of our method is also investigated by utilizing the datasets provided by the plane-wave imaging challenge in medical ultrasound (PICMUS). In addition, an extensive comparison with the commonly used regularization functions in IPB is also presented. The results demonstrate that our method can obtain better image quality in contrast and resolution than other IPB methods. Our proposed method can reach a spatial resolution of 0.34 mm full-width at half-maximum, a contrast-to-noise ratio (CNR) of 18.32 dB, contrast ratio (CR) of 1.99 and generalized CNR (gCNR) of 1.00 for simulation datasets, and 0.47 mm full-width at half-maximum, a CNR of 15.45 dB, CR of 1.96 and gCNR of 0.97 for experimental datasets using a single plane wave. In particular, our method can preserve the structural details of the reconstructed image, which paves the way for accurately extracting the structural information of the ultrasound image.