Optimized source estimation for full waveform inversion in ultrasound computed tomography

Abstract

In full waveform inversion (FWI) for ultrasound computed tomography (CT), choosing the right sound source is essential for generating high-resolution images. We developed an optimized source estimation method for FWI to efficiently reduce the value of any cost function and evaluated its performance using simulation data and measurement data. In our optimized source estimation method, we obtain the sound source as α(k)·f, where f is a sound source (an arbitrary complex value), coefficient α(k) is cos(θ_k)+i·sin(θ_k), k is integer (0, 1, ⋯, N-1), θ_k is 2π/N·k, and the integer value of N is 360. We then determine the coefficient α(k) that minimizes the value of the cost function. In contrast to conventional source estimation, which only minimizes the value of the L2 norm cost function, our proposed source estimation can minimize the values of any cost function, such as the L1 norm or a hybrid of L1 and L2 norms. The advantage of our method is that it can be easily applied to FWI with various cost functions. In this preliminary study, we implemented FWI with the L2 norm cost function and compared the performance of our proposed method with that of the conventional method. In the simulation study, FWI with both the conventional and proposed source estimation methods improved the contrasts of inclusions of a numerical phantom compared to FWI with no source estimation. They both also improved the contrasts of inclusions of a measured oil-gel-based phantom compared to a bent-ray reconstruction method. The absolute mean errors between ROI and true values were 39, 11, and 11 [m/s] for the bent-ray reconstruction method, FWI with the conventional method, and FWI with the proposed method, respectively. In addition, FWI with both the conventional and proposed methods improved the contrasts of a patient’s tumor compared to the bentray reconstruction method. These results demonstrate that FWI with the proposed source estimation method can provide the same contrast and quantitative accuracy as FWI with the conventional source estimation method.