Ultrasound waveform tomography using wave-energy-based preconditioning

Ultrasound waveform tomography using the conjugate gradient method produces images with different qualities in different regions of the imaging domain, partly because the ultrasound wave energy is dominant around transducer elements. In addition, this uneven distribution of the wave energy slows down the convergence of the inversion. Using the Hessian matrix to scale the gradients in waveform inversion can reduce the artifacts caused by the geometrical spreading and the defocusing effect resulting from the incomplete data coverage. However, it is computationally expensive to calculate the Hessian matrix. We develop a new ultrasound waveform tomography method that weights the gradient with the ultrasound wave energies of the forward and backward propagation wavefields. Our new method balances the wave energy distribution throughout the entire imaging domain. This method scales the gradients using the square root of the wave energy of forward propagated wavefields from sources and that of backpropagated synthetic wavefields from receivers. We numerically demonstrate that this new ultrasound waveform tomography method improves sound-speed reconstructions of breast tumors and accelerates the convergence of ultrasound waveform tomography.