Data Augmentation by Wavelet Transform for Breast Cancer Based on Deep Learning

2.1 Breast cancer dataset (BreakHis)

Diagnosis of most tumors relies on histopathological analysis of the tissues, which involves a biopsy, followed by microscopic analysis of the breast tissue [13, 14]. The complete process of the biopsy technique is shown in Figure 2. Under different magnifications, pathologists evaluate the tissue biopsies through the microscope [15]. Thus, we obtain images in three channels red, green, and blue (RGB) [6]. To allow the optimization and evaluation of the utility of the proposed method, we selected a BreaKhis database that was created with the collaboration of the P&D Laboratory-Anatomy Dctal Carcinoma Pathological and Cytopathology, Parana, Brazil (http: /www.prevencaoediagnose.com.br). The dataset is an open-source and is available to community members for use. The BreaKHis database contains 7909 (700x460 pixel) histopathological biopsy microscopic images from 82 patients [11, 15]. The dataset comprises 2480 images of benign tumors and 5429 of malignant tumors, distributed across four magnification tiers (40x, 100x, 200x, 400x). Images are categorized as benign (Adenosis [A], Fibroadenoma [F], Phyllodes Tumor [PT], and Tubular Adenoma [TA]) and malignant (Ductal carcinoma [DC], Lobular Carcinoma [LC], Mucinous Carcinoma [MC] and Papillary Carcinoma [PC]) [11, 16].

Figure 3 shows four magnifications of a single breast tissue section with a benign tumor (BreakHis). The distribution of images between the malignant and benign categories for each magnification is presented in Table 1.

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Figure 2. The complete process of a biopsy

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Figure 3. Benign breast tumor slides [1]

Table 1. Image categorization by benign/malignant categories across various magnifications [1]

2.2 Data augmentation

Effective deep learning training necessitates ample data to avoid overfitting and improve performance, which can be achieved through data augmentation or geometric transformations. Figure 4 reveals an imbalance in the BreakHis database's data distribution across levels. To mitigate biases caused by unequal class distribution, we opted for a wavelet image generation from minority class images, equalizing the number of benign and malignant images. To increase the data, the following procedure has been adopted:

The images were resized from 700×460×3 to 224×224×3 pixels, reducing computational complexity and meeting DenseNet-201 input size requirements [17]. The dataset for each magnification level is split into training (96%) and testing (4%) sets through random shuffling [6]. Balancing the 96% benign and malignant classes involved adding wavelet-generated images to the benign class. Table 2 displays the image count after this balance adjustment. Data augmentation, including flipping, cropping, rotation, scaling, and zooming, was also applied to enhance accuracy and prevent overfitting [14, 18-21]. Examples of augmented images are presented in Figure 5.

Figure 4. Distribution of the BreaKhis classes

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Figure 5. Examples of augmented images

Table 2. Image distribution before and after wavelet transform (DWT)

2.3 Discrete wavelet transform (DWT)

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Figure 6. Mallat's algorithm

The DWT, is a mathematical analysis tool that describes an image in terms of both its spatial and frequency characteristics. It uses filters with different cutoff frequencies. The image is subjected to both a low- pass filter known as a 'step function', and a high-pass filter, known as a 'wavelet function'. These two filters are applied sequentially to the entire image. At the output, we get four frequency bands: the first low-frequency (LL) part is a kind of average of the original signal, called an approximate image, and a downscaled version of the original image and a smooth version. The second part is a set of three high-frequency sub-bands characterized by their spatial orientation (HL (horizontal), LH (vertical), HH (diagonal)). The detail images (HH, HL, and LH) are usually referred to wavelet coefficients and outlines of image regions. This process can be repeated any number of times [22]. Alfred Haar introduced wavelets in 1909 and applied them to represent one-dimensional signals. Stephane G. Mallat extends the application of wavelet transforms to images (or 2D signals). He, therefore, introduced a fast wavelet decomposition/reconstruction algorithm. The algorithm is recursive and mainly based on two operations [23]:

Filtering: Convolution of a signal with a low-pass filter (h0) or a high-pass filter (g0).

Downsampling: Reduces the number of signal samples. In fact, horizontally subsampling (1:2) an image is equivalent to removing one column from two, reducing the number of pixels per row by half. Figure 6 shows the MALLAT algorithm, which can be explained as follows:

Let $S_j$ represent the approximate image at resolution level j, and let $D^X_j$ represent the subband at orientation x (where $x \in\{H, V, D\}$) that is extracted at resolution level j. In the algorithm, the input image $S_j$ is first passed to both high-pass and low-pass filtering. The resulting images are then under- sampled on the lines, and each of the sub-sampled images is again filtered by both high-pass and low-pass filters, resulting in a total of four images. These four images are once again sub-sampled, resulting in four images of the same size: an approximation image $S_{j+1}$ and three detail images $D^X_{j+1}$, where $x \in\{H, V, D\}$ [22, 23].

To generate wavelet images from histopathological images of benign breast cancer, we followed several steps. First, we loaded these images in PNG format. Next, we converted them to grayscale because wavelet decomposition is more effective on one-dimensional grayscale images than on three-dimensional color images with red, green, and blue channels. In grayscale, the wavelet coefficients better capture intensity variations within the image, making details such as contours, textures, and structures more visible in the wavelet coefficients. We specifically chose the ‘bior1.3’ wavelet filter, which belongs to the family of biorthogonal wavelets, because it strikes a balance between efficiency and precision, making it suitable for image decomposition. ‘bior1.3’ consists of a low-pass filter (h0) and a high-pass filter (g0). The low-pass filter captures approximation components (low frequencies), while the high-pass filter detects details (high frequencies). Finally, we obtained the wavelet coefficients (LL, LH, HL, HH). The LL coefficient represents low-frequency approximation, containing the overall intensity variations within the image. In other words, it captures the general structures and trends of the image. Meanwhile, LH, HL, and HH represent high-frequency details in different directions, revealing fine contours, textures, and structures of the image. Together, these coefficients allow us to decompose the image into spatial frequencies and orientations, providing a rich representation for analysis and characterization [12].

Figure 7 illustrates the histology image after performing wavelet transform (DWT).

Figure 7. An example of applying the wavelet transform (DWT) to BreakHis images

4.1 Experimental setting

Figure 10 and Figure 11 represent the simulation results of the learning process. Various hyperparameters are utilized to train the proposed framework.

Weights trained: The proposed model utilizes pre-trained ImageNet weights at the beginning of the network.

Optimizer function: We chose RMSprop as the Optimizer function.

Loss function: The categorical cross-entropy metric, commonly applied in classification tasks involving two or more label classes, is employed as the evaluation metric to calculate the difference between two probability distributions (0 and 1).

Activation function: After training, classification is performed employing the Softmax activation function, which produces a vector of probabilities for each sample of the predicted class length.

Dropout: To improve network performance, a dropout layer was applied with a probability of P=0.5.

Early stopping: A learning rate at 1e-7 is used to decrease the loss function and gradually lowered to approach zero.

Furthermore, a batch size of 35 was used and the training consists of 100 epochs.

Figure 10. BreakHis dataset training progress independent of magnification factors

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Figure 11. Training progress of BreakHis dataset based on its magnification factors (40X, 100X, 200X, and 400X)

4.2 Performance metrics

Common statistical parameters are utilized to evaluate the performance of the proposed method.

These parameters are based on various metrics that are derived from the elements of the confusion matrix. The metrics correspond to four terms, namely true positive (TP), false positive (FP), false negative (FN), and true negative (TN).

One can express the computation and evaluation of these statistical metrics as follows:

$Accuracy =\frac{T P+T N}{T P+T N+F P+F N}$                     (2)

$\text{Pr }ecision =\frac{T P}{T P+F P}$                    (3)

$\operatorname{Re}call =\frac{T P}{T P+F N}$                  (4)

$F1-score=2 * \frac{( { precision } * \text {Re }call)}{T P}$                   (5)

4.3 Discussion

Figure 12 and Table 3 respectively present the full report of our classification approach applied to the breast cancer test set and the ROC curve used for the diagnostic evaluation of breast cancer. The BreakHis dataset comprises 7909 microscopic images of breast tumor tissue, across various magnification factors (40x, 100x, 200x, and 400x). It encompasses 2480 benign samples and 5429 malignant samples. Notably, each magnification factor exhibits a class imbalance, with a higher count of malignant samples compared to benign ones. To address this, additional wavelet-generated images were introduced into the benign class. With an imbalanced dataset, the majority classes are consistently classified correctly more often than the minority classes. Wavelet balancing has helped mitigate this effect by providing more data for the minority class, thus improving the chances of accurate classification. From Table 3, our approach yields excellent results in both magnification-independent and magnification-specific binary classifications. It's noteworthy that 212 and 218 microscopic images are accurately diagnosed with Magnification Independence. Only five benign microscopic images were misclassified, with no malignant images misclassified by our model. The key concern is to avoid misclassifying malignant cancer as benign, as it could result in harm due to missed opportunities for early treatment if symptoms arise, creating a false sense of security. The magnification-independent approach showcases outstanding performance, achieving an overall accuracy of 99%, highlighting the model's robustness in accurately classifying samples regardless of magnification scale. For the benign class, the model exhibits high precision and Recall of approximately 98%, along with an F1-Score of 99%, indicating reliable identification of benign samples and effectively capturing 98% of actual benign cases. Similarly, for the malignant class, the model exhibits a precision of approximately 98%, a perfect recall of 100%, and an F1-Score of 99%. These results highlight the remarkable consistency of the model in detecting real malignant cases. Based on the ROC curve in Figure 11, we achieved a remarkable accuracy of 99.98%, indicating the model's exceptional stability. It can be observed from Table 3 that a total of 0, 1, 0, and 0 microscopic images are false negative classified for 40x, 100x, 200x, and 400x breast cancer categories, respectively. A total of 1, 0, 1, and 1 microscopic image are misclassified for the malignant class for 40x, 100x, 200x, and 400x breast cancer categories, respectively. Displaying an outstanding overall accuracy of 99% across all scales, these results highlight the consistent robustness of the model, reinforcing its reliability for early cancer detection. For the benign class, high performances are maintained at each scale, with respective precisions of 96%, 100%, 96%, and 96%. A high Recall of 96% for the 100x magnification and 100% for other scales confirms the model's ability to effectively capture all real benign cases. F1 scores, reaching 98%, indicate an optimal balance between precision and Recall for this class. Similarly, for the malignant class, the model exhibits perfect precisions of 96% at 100x magnification and 100% at other scales, demonstrating its reliable identification of malignant samples. High Recalls, ranging between 98% and 100%, underscore the successful detection of the vast majority of real malignant cases. F1 scores, averaging at 99%, highlight the model's excellent performance across all magnifications. These overall performances demonstrate the robustness of the cancer detection model, showcasing its promising potential for practical application in cancer detection. A comparison between existing literature works and our approach to the classification task of BreakHis images based on similar conditions has been summarized in Table 4.

Table 3. Full classification report of our classification approach applied to the breast cancer test set

Table 4. A comparison of the proposed framework with other methods on the BreaKHis dataset for the classification task