## 1 Introduction  
Breast cancer in women is an important health problem for both developed and developing countries. A recent report by the Cancer Statistics Center of the American Cancer Society shows that among the estimated new cancer cases in 2020, the number of cases of breast cancer is 1,806,590. It also shows that around 606,520 cancer deaths are anticipated only in the United States, of which breast cancer contributes to around 279,100 (approximately 46%) [1]. Breast ultrasound (US) imaging is one of the most promising tools to distinguish and classify breast tumors among the other imaging techniques such as mammograms, MRIs, etc. Ultrasonic images are constructed by dispersing pulses of ultrasound into human tissue using a probe. In US imaging, the pulses echo off the body tissues having several reflection properties which are recorded and exhibited as an image. The B-mode or brightness mode image, in turn, shows the acoustic impedance of a cross-section of tissue in two dimensions. Plenty of studies have been carried out and are still running to achieve higher accuracy in automatically differentiating malignant breast tumors from benign ones. In 2002, [PERSON] et al. [2] used the depth-to-width ratio of the region of a lesion, the normalized radial gradient, autocorrelation in the depth of lesion region, and minimum side difference of the lesion boundary for the detection of breast tumors. In 2007, [PERSON] et al. [3] presented a computer-aided diagnostic (CAD) system where a few geometric features such as shape, orientation, margin, lesion boundary, echo pattern, and posterior acoustic feature are used. They reported an accuracy of 91.7%. However, in their work, the segmentation of lesions was performed both manually and automatically from the normal breast tissue, making it complicated for vast data of US images. In recent years, multi-resolution transform domain-based methods using US images showed higher promise in automatic breast tumor classification tasks. In 2017, [PERSON] et al. [4] employed an empirical mode decomposition (EMD) method with discrete wavelet transform (DWT) followed by a wrapper algorithm to obtain a set of non-redundant features for classifying breast tumors and reported an accuracy of 98.01% on their database. Unfortunately, traditional DWT has limited directional information with the directions being only along with horizontal, vertical, and diagonal dimensions. In 2019, [PERSON] et al. [5] used a gray level concurrency matrix (GLCM) algorithm with linear SVM to classify benign and malignant tumors. [PERSON] et al. [6] presented a comparative study between two multi-resolution transform domain-based techniques, namely, wavelet and curvelet, for breast tumor diagnosis in digital mammogram images. Contourlet transform, another multi-resolution transform domain-based technique [7], is providing more directional information, with various directional decomposition levels increasing along with the increase of the pyramidal decomposition levels. It has also shown to be a better descriptor of arbitrary shapes and contours compared to wavelet transform. Contourlet-based mammography mass classification is reported in [8; 9]. It is to be noted that there are many concerns about performing mammography, which utilizes low-energy X-ray radiation, for regular checkups. Moreover, in mammography, many women have to go through unnecessary breast biopsies due to a lack of specificity. In benign cases, this figure is about 65-85% of unnecessary breast biopsies [10]. This unnecessary biopsy causes patients emotional and physical burdens by increasing the unexpected cost of mammographic screening which can be easily avoided. For that reason, researchers have recently been putting their efforts into relatively safer approaches like ultrasonography and elastography. In [11], Contourlet transform is employed on ultrasound shear-wave elastography (SWE) images where Contourlet-based texture features were used with Fisher classifier for classification purposes and reported an accuracy of 92.5%.