Wavelet-like selective representations of multidirectional structures: a mammography case

The subject of this paper is selective representation of informative texture directionality in sparse domain of four verified multiscale transforms: contourlets, curvelets, tensor and complex wavelets. Directionality of linear or piecewise linear structures is a fundamental property in recognition of anatomical structures, i.e. separating the brain regions, directional characteristics of small coronary arteries. Another important example is spicule extraction in mammograms which is based on directional analysis of malignant spiculated lesions. The originality of the proposed experiments lies in optimization of multiscale wavelet-like representations to differentiate multidirectional structures of architectural distortions and spiculated masses in low-contrast noisy mammograms. For that purpose, the applied method consists in proposed phantom-based normalization and defined assessment criteria of directional information activity. The directional activity including both measures of angular resolution and angular selectivity was determined relative to increased background density and noise simulating reduced perceptibility of the analyzed objects. A numerically modeled phantom of multidirectional linear structures was used to assess subjectively and objectively the efficiency of nonlinear approximation for radially diverging spicule-like structures. Size and distribution of the structures simulates essential nature of spiculated signs of breast cancer. Basing on the experimental results, the complex wavelet domain was concluded to be the most effective tool to uniquely represent relevant information in the form of multidirectional piecewise linear structures in low-contrast noisy mammograms.