Extending the convergence limit of nonlinear speed of sound reconstructions towards common ultrasonic frequencies

Nonlinear speed of sound reconstructions based on the Kaczmarz method are acquiring quantitative tomographic data by using ultrasonic measurements. However, the gradient descent algorithm used to do so is claimed to be limited to low frequencies due to phase ambiguities of the gradient. This convergence limit was derived by Natterer. Here, we propose a method using frequency filtering to overcome the convergence issue. By applying a low pass filter to the gradient factors, the reconstruction can be performed at common ultrasound frequencies. First numerical results demonstrate that the frequency range is extended by a factor of three for the chosen phantom.