This study proposes a Hessian-inversion-free ray-born inversion approach for biomedical ultrasound tomography. The proposed approach is a more efficient version of the ray-born inversion approach proposed in [3]. Using these approaches, the propagation of acoustic waves are modelled using a ray approximation to heterogeneous Green's function. The inverse problem is solved in the frequency domain by iteratively linearisation and minimisation of the objective function from low to high frequencies. In [3], the linear subproblem associated with each frequency interval is solved by an implicit and iterative inversion of the Hessian matrix (inner iterations). Instead, this study applies a preconditioning approach on each linear subproblem so that the Hessian matrix becomes diagonalised, and can thus be inverted in a single step. Using the proposed preconditioning approach, the computational cost of solving each linear subproblem of the proposed ray-Born inversion approach becomes almost the same as solving one linear subproblem associated with a radon-type time-of-flight-based approach using bent rays. More importantly, the smoothness assumptions made for diagonalising the Hessian matrix make the image reconstruction more stable than the inversion approach in [3] to noise.

翻译：本研究提出了一种无海森矩阵逆的射线-玻恩反演方法，用于生物医学超声层析成像。该方法是文献[3]中射线-玻恩反演方法的一种更高效版本。采用这些方法时，声波传播通过射线近似非均匀格林函数进行建模。反问题在频域中通过从低频到高频迭代线性化并最小化目标函数来求解。在文献[3]中，每个频率区间对应的线性子问题通过隐式迭代求逆海森矩阵（内迭代）进行求解。而本研究对每个线性子问题施加预处理方法，使得海森矩阵对角化，从而能够单步求逆。采用所提出的预处理方法后，所提射线-玻恩反演方法中每个线性子问题的计算成本几乎与基于弯曲射线的拉东型飞行时间方法中求解一个线性子问题的计算成本相当。更重要的是，为对角化海森矩阵所做的平滑性假设使得图像重建对噪声的稳定性优于文献[3]中的反演方法。