## 1 Introduction
Contourlet transform was also employed in [12] on B-mode US, shear wave elastography (SWE), and contrast-enhanced US (CEUS) images, and it reported an accuracy of 67.57%, 81.08%, and 75%, respectively. Both DWT and curvelet transforms are not capable of providing a variety of directions and also do not have good directional selectivity in two dimensions as compared to the Contourlet transform. Many researchers, rather than trying to extract various features from the original B-mode images, had tried to use statistical modeling such as Gaussian or Nakagami models to create parametric models of the images [13; 14] and found satisfactory results. The primary inspiration behind these types of statistical methods is to mathematically model the scattering of sound waves through the tissues, which can provide more insight into the system and, thus, provide more accurate features. Moreover, statistical modeling can describe the false positive (FP) and false-negative (FN) more precisely than spatial domain visual ultrasound images. [PERSON] et al. [15] used Nakagami modeling to address the detection of liver fibrosis in rats, which might be different from breast tumor classification, but it does provide some validation to the usefulness of parametric imaging. A recent trend in this field is the application of deep learning-based neural networks such as CNN as a potential tool for the automated analysis of different types of medical images, allowing the easy and robust diagnosis of various types of medical ailments. Unlike the traditional feature engineering-based techniques, whose accuracies depend on the robustness of the feature extraction algorithms, deep neural networks allow the implementation of extremely efficient and highly accurate automated medical tools, especially for the automated classification of breast tumors [16] if provided with enough data and resources. [PERSON] et al. [17] applied CNN and morphology information extraction methods on shear-wave elastography data for breast tumor classification. [PERSON] et al. [18] also employed CNN for breast tumor classification, but they applied it directly on breast ultrasoundimages. [PERSON] et al. [19] used a generative adversarial network (GAN) along with CNN for breast tumor segmentation and classification using ultrasound images with satisfactory outcomes. [PERSON] et al. [20] used a simple neural network that is cheap and easy to use and gained a satisfactory result in a small online dataset. [PERSON] et al. [21] proposed an on-device AI pre-trained neural network model which can train the CNN classifier on a portable device without a cloud-based server. [PERSON] et al. [22], in their work, illustrated a neural network with faster R-CNN and ResNet-101. [PERSON] et al. [23] presented a method of US to RGB conversion and fine-tuning using back-propagation. [PERSON] et al. [24] illustrated a novel approach of Deep CNN with multi-scale kernels and skip connections. However, the deep neural network methods do not take the statistical properties or characteristics into account. In this work, the Rician Inverse Gaussian (RiIG) distribution [25] is shown to be highly suitable for modeling the statistics of the Contourlet coefficient images. It is shown that features (statistical, geometrical, and texture-based) extracted from the RiIG parametric images provide more accuracy for breast tumor classification than the features extracted from US B-mode images. Parametric (P) images are obtained by replacing a pixel with the RiIG parameter (8), estimated over a local neighborhood of the corresponding pixels where the center of that neighborhood is considered for the requested parameter. Thus, the pixel values are mapped (8-map) into the parameter values which provide the parametric image. To enhance the incorporation of the statistical characteristics in classification, WCP images are introduced.