The method of one embodiment for multi-grid tomographic inversion tissue imaging comprises receiving acoustic waveform data characterizing a volume of tissue, determining and refining models of the distributions of a first and second acoustomechanical parameter within the volume of tissue using a series of grids with progressively finer discretization levels, and generating an image based on at least one of the refined models of the first and second acoustomechanical parameters. The system of one embodiment for multi-grid tomographic inversion tissue imaging comprises ultrasound emitters configured to surround and emit acoustic waveforms toward a volume of tissue, ultrasound receivers configured to surround tissue and receive acoustic waveforms, and a processor configured to determine and refine models of the distributions of a first and second acoustomechanical parameter within a volume of tissue, and generate an image based on at least one of the refined models of the first and second acoustomechanical parameters.
