Microwave examination of individuals is carried out by transmitting microwave signals from multiple antenna locations into an individual and receiving the backscattered microwave signals at multiple antenna locations to provide received signals from the antennas. The received signals are processed to remove the skin interface reflection component of the signal and the corrected signal data are provided to a hypothesis testing process. In hypothesis testing for detecting tumors, image data are formed from the test statistic used to perform a binary hypothesis test at each voxel. The null hypothesis asserts that no tumor is present at a candidate voxel location. The voxel threshold is determined by specifying a false discovery rate to control the expected proportion of false positives in the image. When the test statistic value associated with a voxel is greater than the threshold, the null hypothesis is rejected and the test statistic is assigned to the voxel. For voxels where the test statistic falls below the threshold, the null hypothesis is accepted and the voxel value is set to zero. The resulting image indicates the locations or other characteristics of detected tumors.