Detection of breast cancer using fractional discrete sinc transform based on empirical Fourier decomposition

Breast cancer is the most common cause of death among women worldwide. Early detection of breast cancer is important; for saving patients' lives. Ultrasound and mammography are the most common noninvasive methods for detecting breast cancer. Computer techniques are used to help physicians diagnose cancer. In most of the previous studies, the classification parameter rates were not high enough to achieve the correct diagnosis. In this study, new approaches were applied to detect breast cancer images from three databases. The programming software used to extract features from the images was MATLAB R2022a. Novel approaches were obtained using new fractional transforms. These fractional transforms were deduced from the fraction Fourier transform and novel discrete transforms. The novel discrete transforms were derived from discrete sine and cosine transforms. The steps of the approaches were described below. First, fractional transforms were applied to the breast images. Then, the empirical Fourier decomposition (EFD) was obtained. The mean, variance, kurtosis, and skewness were subsequently calculated. Finally, RNN-BILSTM (recurrent neural network-bidirectional-long short-term memory) was used as a classification phase. The proposed approaches were compared to obtain the highest accuracy rate during the classification phase based on different fractional transforms. The highest accuracy rate was obtained when the fractional discrete sinc transform of approach 4 was applied. The area under the receiver operating characteristic curve (AUC) was 1. The accuracy, sensitivity, specificity, precision, G-mean, and F-measure rates were 100%. If traditional machine learning methods, such as support vector machines (SVMs) and artificial neural networks (ANNs), were used, the classification parameter rates would be low. Therefore, the fourth approach used RNN-BILSTM to extract the features of breast images perfectly. This approach can be programed on a computer to help physicians correctly classify breast images.