Bayesian approaches to sonar performance prediction and breast tumor diagnosis using microwave measurements

The development of effective sonar systems depends on the ability to predict accurately the performance of sonar detection and localization algorithms in realistic ocean environments. Such environments are typically characterized by a high degree of uncertainty, thus limiting the usefulness of performance prediction approaches that assume a known environment. Using a statistical model of environmental uncertainty, we derive analytical receiver operating characteristic (ROC) expressions and probability of correct localization (PCL) expressions for predicting the performance of optimal and sub-optimal sonar detection and localization algorithms in uncertain environments. We used data collected during the SWellEx-96 experiment and simulated data generated from an NRL benchmark shallow water model to assess the validity of the performance expressions. The results showed that (1) Bayesian detection performance primarily depends on the signal-to-noise ratio, the rank of the signal matrix that captures the effect of environmental uncertainty, and the signal-to-interference coefficient; (2) Bayesian localization performance is primarily determined by the signal-to-noise ratio, the effective correlation coefficient between the signal wavefronts that in part captures the effect of environmental uncertainty, and the number of hypothesized source positions; (3) the proposed analytical performance expressions illustrate the importance of and tradeoffs between fundamental parameters for sonar performance; and (4) it is possible to perform sonar performance prediction much faster than with commonly used Monte Carlo methods.; An optimal Bayesian signal detection framework is developed for the detection and localization of breast tumor using microwave measurements. The proposed likelihood ratio detection algorithm incorporates the prediction of the random field of the electromagnetic (EM) measurements using a forward EM propagation model and a 2D Markov random field (MRF) model that characterizes the spatial properties of both benign and malignant breast tissue permittivity. With simulated data, the ROC and PCL curves for the proposed algorithm were illustrated as a function of local uncertain tissue permittivity characteristics, and tumor contrast, size, and shape, and were demonstrated improvements over the algorithms that optimally post-process a reconstructed image. Simulation results also indicate the convergence of the estimation of the MRF model parameters and the effect of the sensor array configuration on tumor detection performance.