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Visual inspection of ultrasound is diagnostically limited for characterizing breast tissue, in particular when it comes to visually detecting hyperplasia that forms in the ducts at its early formation (at submillimeter resolution) stages. It can, of course, be seen using biopsies. But this will not be done unless the areas have been flagged using noninvasive modalities. The aim of this paper is to draw to the attention of the medical community (albeit through simulations) that the continuous wavelet transform decomposition (CWTD) that was proven in vivo for tissue characterization before has the potential to flag out simulated hyperplasia data at submillimeter resolutions. And it might be an excellent candidate for detecting in vivo hyperplastic changes in the breast. To the best of our knowledge, this is the first attempt at studying the potential of detecting cell growth in breast ducts using ultrasound. The stochastic decomposition model (the CWTD) of the RF echo with its coherent and diffuse components, yields image parameters that correlate closely with the structural parameters of the (simulated) hyperplastic stages of the breast tissue. The discrimination power of the various parameters is studied under a host of conditions, such as varying resolution, depth, and coherent to diffuse energy ratio (CDR) values using a point-scatterer model simulator that mimics epithelium hyperplastic growth in the breast ducts. These are shown to be useful for detecting the various types of simulated hyperplastic data. Careful analysis shows that three parameters, in particular the number of coherent scatterers, the Rayleigh scattering degree, and the energy of the diffuse scatterers, are most sensitive to variations in the hyperplastic simulated data. And they show very high ability to discriminate between various stages of simulated hyperplasia, even in cases of low resolution and low CDR values. Using the area under the receiver operating characteristics (ROC) curve (A- - z) as the performance metric, values of Az > 0.942 are obtained when discriminating between stages for resolution les 0.4 mm, even for low CDR values. Then it drops below the 0.9 range as the resolution exceeds the 0.4-mm range. A nonparametric segmentation method to extract ductal areas from breast scans is presented to be used as a pre-step before classification of hyperplastic stages in breast ducts. This is a necessary step for segmenting the RF scan into ductal versus nonductal areas from breast scans. This is tested using breast tissue mimicking phantom data resulting values of Az > 0.948 for different duct densities.