Abstract: Improved acoustic tomography is provided using an array of transducer modules that surround the target, Each transducer module is a phased array of acoustic transducer elements that provides a steerable plane wave or steerable diverging wave excitation to the target. Tomographic reconstruction of the resulting data sets is substantially less computationally demanding than tomographic reconstruction of conventional acoustic tomography data sets, enabling image frame rates of 10 per second or better. This approach can be combined with dual modality imaging In cases where hardware limitations lead to undesirable gaps between the transducer modules, virtual receiver elements can be defined at locations between the transducer modules. By estimating signals that would be received at locations of the virtual receiver elements, the undesirable effects of these gaps can be reduced.