Fused Microwave and Ultrasonic Breast Imaging Within the Framework of a Joint Variational Bayesian Approximation

Early diagnosis of breast tumors can, in principle, be achieved by jointly running electromagnetic and acoustic probings, more precisely microwave (MW) and ultrasound (US). Indeed, such modalities are noninvasive, nonionizing, and low cost and proceed without registration for free pending breasts, not like other joint modalities that impose compression. Because of the strongly contrasted electromagnetic parameters of breast constituents, MW yields high-contrast images of low resolution and converse with the US when faced with weakly refracting elements. The key benefit is the common breast structure, and fusion should produce images with both high contrast and resolution. A Bayesian formalism is chosen, and an unsupervised joint variational Bayesian approximation (JVBA) is developed. In that, edges' hidden variables and hyperparameters are automatically tuned along with the optimization. The mathematics is detailed in a general setting of fusion, and then, one proposes imaging of realistic MRI-derived breast slices. A wealth of numerical simulations from noisy single-frequency MW and multiple-frequency US data preserved from inverse crime yields means (i.e., breast maps) and variances of the unknown electromagnetic and acoustic parameter distributions as probabilistic realizations, evolutions of hyperparameters, as well as global indicators of accuracy. Comparisons with a joint contrast-source inversion edge-preserving (JCSI-EP) developed earlier in a deterministic framework illustrate the methodology.