Optimally weighted wavelet transform based on supervised training for detection of microcalcifications in digital mammograms

We are developing a computer-aided diagnosis (CAD) scheme for detection of clustered microcalcifications in digital mammograms. The use of an empirically chosen wavelet and scale combination for detection of microcalcifications as an initial step of the CAD scheme has been reported by us previously. In this study, we developed a technique for optimizing the weights at individual scales in the wavelet transform to improve the performance of our CAD scheme based on the supervised learning method. In the learning process, an error function was formulated to represent the difference between a desired output and the reconstructed image obtained from weighted wavelet coefficients for a given mammogram. The error function was then minimized by modifying the weights for wavelet coefficients by means of a conjugate gradient algorithm. The Least Asymmetric Daubechies' wavelets were optimized with 297 regions of interest (ROIs) as a training set by a jackknife method. The performance of the optimally weighted wavelets was evaluated by means of receiver-operating characteristic (ROC) analysis by use of the above set of ROIs. The analysis yielded an average area under the ROC curve of 0.92, which outperforms the difference-image technique used in our existing CAD scheme, as well as the partial reconstruction method used in our previous study.