This application presents a system and related methods that analyze a volume of tissue using ultrasound waveform tomography imaging. By using frequency-domain waveform tomography techniques and a gradient descent algorithm, the system can reconstruct the sound speed distributions of a volume of tissue, such as breast tissue, of varying densities with different types of lesions. By allowing sound speed to have an imaginary component that characterizes sound attenuation, the system can classify the different types of lesions with a fine granularity.