An archetype signal dependent noise (SDN) model is a component used in modeling image acquisition systems. This component may share properties with stationary normal white noise (WN). The characterization of WN images was used as a reference for making comparisons with SDN in both the image and Fourier domains (FDs). The image domain (ID) wavelet expansion was applied to WN images (n = 1000). Expansion-image orthogonality conditions were used to model and characterize the variance decomposition in both domains. Aside from the wavelet analysis, FD components of WN were characterized with summarized distributions and probability density function modeling. SDN was constructed by either multiplying simulated mammograms (i.e., stochastic images with 1/f2α power spectra) or clinical mammograms (both with n = 1000) with WN. SDN was analyzed with the same techniques applied to WN. The variance decomposition for WN decreases exponentially as a function of the ID wavelet expansion level as did SDN; expansion images for both types of noise were distributed similarly in the Fourier plane. Theoretically, the Fourier transform of normal WN produces a complex normally distributed image in the FD with a uniform power spectrum distributed exponentially; SDN has similar attributes. These findings are counterintuitive as SDN can be nonstationary in the ID but have stationary attributes in the FD.

Abstract We illustrate the connection between image-texture and defined regions in a polar spatial frequency coordinate system. This is provided within the context of describing a non-parametric method for characterizing two-dimensional spectra of gray scaled images, described in part previously. The spectrum is divided into concentric radial bands of fixed bandwidth. Each band is summarized, producing a set of measures characterizing the image as a function of radial spatial frequency. This set of measures has a parallel multiscale description as texture in the image domain. This approach was modified to capture texture with directional attributes. This is a data reduction technique that gives a full accounting of the image variance as function of image texture and direction indexed to regions in the polar frequency plane. Application examples include analyzing the summarized spectrum graphically, making inter/intra image spectral comparisons, and evaluating spectral models. Simulated noise images, an image of peppers, and a gray scale image with well-defined linear structure were used to illustrate the principles.