Fourier analysis of signal dependent noise images.

An archetype signal dependent noise (SDN) model is a component used in analyzing images or signals acquired from different technologies. This model-component may share properties with stationary normal white noise (WN). Measurements from WN images were used as standards for making comparisons with SDN in both the image domain (ID) and Fourier domain (FD). The ID wavelet expansion was applied to WN images (n = 1000). Orthogonality conditions were used to parametrically model the variance decomposition, as described in both domains. FD components were investigated with probability density function modeling and summarized measures. SDN images were constructed by multiplying both simulated and clinical mammograms (both with n = 1000) by WN. The variance decomposition for both WN and SDN decreases exponentially as a parametric function of the ID expansion level; expansion image variances for both types of noise were captured similarly in the Fourier plane corresponding with the ID parametric model. The Fourier transform of WN has a uniform power spectrum distributed exponentially; SDN has similar attributes. Fourier inversion of the lag-autocorrelation performed in the FD produced a statistical estimation of the SDN's image factor. These findings are counterintuitive as SDN can be nonstationary in the ID but have stationary attributes in the FD.