## 1 Introduction
The WCP images are constructed by multiplying the Contourlet Parametric (CP) images (i.e., parametric images obtained from the Contourlet coefficients of images) with their corresponding Contourlet transformed coefficient images. Here, the term \"weighted\" is being used in this scheme because all the parameters of CP images were getting weighted by multi-plication with their corresponding Contourlet coefficient images. In our work, the WCP images are utilized for breast tumor classification in both feature extraction-based approach and convolutional neural network (CNN) based approach. In both approaches, the features extracted from WCP images are subjected to various classifiers such as the support vector machine (SVM), k-nearest neighbors (KNN), fitted binary classification decision tree (BCT), fitted error-correcting output codes (ECOC) model, binary Gaussian kernel classification model (BGKC), linear classification models for two-class (binary) learning with high-dimensional (BLHD), the fitted ensemble of learners for classification (ELC), etc. From the results, it is shown that the features extracted from the WCP images provide the highest accuracy compared to the original US B-mode images, parametric (P) images, Contourlet transformed images and CP images. It is to be noted that this work is the first one to investigate the effectiveness of WCP images for breast tumor classification. For the CNN-based approach, the WCP images of six Contourlet sub-band coefficients are concatenated to form a six-channel 3D stack image and then fed to the neural network, with the same seven classifiers applied on the output side. New neural network architecture is proposed instead of using the available pre-trained networks, since the pre-trained networks are built for 1-channel or 3-channel visual images with spatial dimensions, and thus, they are not compatible with our 6-channel 3D stack of transform domain Contourlet sub-band coefficients. The performance of the prior classifiers is tested on three datasets of US images for breast tumor classification and compared with existing methods. The main contributions of this work are listed below:  
* This paper demonstrates the suitability of Rician inverse Gaussian (RiIG) distribution [25] for statistical modeling of the Contourlet transformed breast ultrasound images. Further, it shows that the RiIG distribution is better than the well-known Nakagami distribution in capturing the statistics of Contourlet transformed breast ultrasound images in breast tumors classification. * The suitability of WCP images in classifying breast tumors is investigated for the first time employing three different publicly available datasets consisting of 1193 B-mode ultrasound images and shows that a very high degree of accuracy can be obtained in breast tumor classification using traditional machine-learning-based classifiers as well as deep convolutional neural networks (CNN). * A new deep CNN architecture is proposed for the classification of breast tumors based on RiIG modeled WCP images for the first time. It is also shown that the efficacy of the CNN architecture is superior to the classical feature-based method.