Ultrasound tomography with learned dictionaries
The images produced by MRI scan and sound speed images depict similar structures in the breast. Although these two imaging modalities rely on totally different physical principles (magnetism versus acoustics) they trace similar structures because both water content (measured by MRI) and sound speed (measured by UST) increase with tissue density. The high degree of spatial correlation of MR and sound speed images is therefore largely driven by similar sensitivity to changes in tissue density. However, UST imaging is an ill-conditioned problem, which requires a proper regularization approach to assure a reliable and accurate reconstruction. Assumption that an image has a sparse representation in an overcomplete dictionary can be used as an efficient regularization constraint for image reconstruction from ill-conditioned systems.
To obtain the dictionary adapted to the statistical properties of medical breast images (MRI and UST), we have applied the maximum likelihood dictionary learning method on the CURE database of MRI breast scans. The main steps of the algorithm can be outlined as follows.