Medical images can be described by their power and phase spectra. Therefore, it is of interest to know how these components influence human observers in detection tasks. Whereas the power spectrum appears to correctly describe the useful statistical properties of computer generated noise images (like white noise, filtered white noise or lumpy backgrounds), this might not be the case for patient structured images. The present study investigates the role of stationarity, power and phase spectra of two types of medical images (mammography and angiography). We consider different categories of images that all have the same mean, and power spectrum. Two-alternative forced-choice experiments are performed on patient structured images, random phase, filtered white noise, and clustered lumpy background. This latter has the property to contain visible structures similar to the ones observed on real mammograms, and (unlike real patient structure) to be stationary by construction. It is shown that model observers can take non-stationarity into account of real images in two different ways. The safest and easiest way consists of applying the model template directly on the images. The other way consists of correcting the performance computed from global quantities with a factor that takes into account local statistical values in the area of interest. Finally, patient structured backgrounds are not fully described by their power spectrum and we show that human observers are able to use some information contained in the phase spectrum.