Ultrasound waveform tomography with a spatially-variant regularization scheme

Regularization is often needed in breast ultrasound waveform tomography to improve tomographic reconstructions. A global regularization parameter may lead to either over-regularization or under-regularization in different regions in the imaging domain. We develop a new ultrasound waveform tomography method with spatially-variant regularization. Our new method employs different regularization parameters in different regions of the breast so that each regularization parameter is optimal for the local region. Our numerical examples demonstrate the improvement of ultrasound waveform tomography using the spatially-variant modified total-variation regularization for sound-speed reconstructions of large and small breast tumors, particularly when their sizes are significantly different from one another.