In digital mammograms, an early sign of breast cancer is the existence of microcalcification clusters (MCs), which is very important to the early breast cancer detection. In this paper, a new approach is proposed to classify and detect MCs. We formulate this classification problem as sparse feature learning based classification on behalf of the test samples with a set of training samples, which are also known as a “vocabulary” of visual parts. A visual informationrich vocabulary of training samples is manually built up from a set of samples, which include MCs parts and noMCs parts. With the prior ground truth of MCs in mammograms, the sparse feature learning is acquired by the
Breast cancer is the most common tumor disease in women, with the increasing incidences in recent years. And also, it is one of the major death causes among middleaged women in the world. Currently, digital mammograms are one of the most reliable methods to perform the early diagnosis, which is very important for the effectiveness of treatment methods.
In digital mammograms, an important sign of the early breast cancer is the existence of MCs. They always exist in 30%–50% of mammographically diagnosed cases, which are present with tiny bright spots of different morphology. Microcalcifications are small calcifications with different shapes and densities, approximately 0.1–1 mm in diameter. Isolated microcalcifications are not dangerous, but a microcalcification cluster might be an early sign of breast cancer [
However, there is only about 3% of useful information in mammograms, which can be seen by doctors with the naked eye. Due to the fact that most details in mammograms cannot be perceived by human eyes, it is even very difficult for a skillful radiologist to find the sign of early breast cancer, that is, MCs, as a result missing the best time for treatment. So, one of the key techniques for early diagnosis of the breast cancer is to detect MCs and to judge whether they are malignant or not in mammograms.
According to recent researches, there are several existing criteria to characterize the MCs shape properties. Among them, one of the well known is the category criterion proposed by Le Gal et al. [
Le Gal’s MCs classification standards. Type I: annular; Type II: regularly punctiform; Type III: dusty; Type IV: irregularly punctiform; Type V: vermicular calcification.
Up till now, computer aided diagnosis (CAD) is still a useful tool in breast cancer detection to improve the accuracy of radiologists and to help radiologists to read mammogram films. It may provide good help to radiologists in interpreting mammograms to detect MCs and classify them into malignancy or not. A large number of researchers in this field have been trying to find effective methods to automatically detect MCs and categorize them as normal, benign, or malignant.
Because it is very important in breast cancer diagnosis, the detection accuracy of MCs has become a crucial application task and research. Recently a lot of methods have been developed. These approaches have been also greatly assisting radiologists and doctors in diagnosing the disease [
However, how to successfully apply the mammography technology to detect breast cancer and design a breast cancer detection system greatly depends on the careful designing of the two important modules: feature selection and sample classification. A lot of wellestablished methods have been proposed to address this challenge problem. According to [
To detect the early sign of this disease and to aid doctors to diagnose breast cancer in early stage, a novel approach for MCs classification is proposed based on sparse feature learning and representation with TWSVMs, which is inspired by the recent progress in
Especially, to extract highlevel and conceptual information, for example, the existence of an MC in a mammogram block, it is very important for us to convert the lowlevel input, such as the pixel value, to highlevel and more meaningful representations. Through this transformation, the feature learning and detection process will be well constructed.
Ideally, a test example can be represented just from the training samples of the same category. Therefore, when the test sample is expressed as a linear combination of the entire training sample, the coefficient vector will be sparse. That is, there will be relatively few nonzero coefficients in the vector. Test samples from the same category will have a similar sparse representation, while test samples from different categories will lead to different sparse representations. So the sparse representation coefficients can be treated as the more meaningful and discriminant information for the samples classification. In order to get the sparse coefficient vector, we use
To achieve a good performance for MCs detection, we designed two methods to achieve the goal of the detection system. The first one is the sparse discriminant analysis algorithm, which is achieved by computing the residuals of sparse coefficients of the test sample between the centroid sparse coefficients of training samples. As we have known traditional supervised learning methods always use a training procedure to create a classification model for testing. But the proposed sparse representation based approach does not contain the separate training and testing sections. We directly achieved the classification goal out of the testing samples’ sparse representation according to the training samples. Another unique feature of the new method is that no model selection is needed. The second one is designed by the combination of sparse representation and the stateoftheart classifier TWSVMs. We employ the sparse representation approach as a feature learning method in terms of the coefficient vector for samples feature extraction, and then we feed it with the trained TWSVMs to formulate the detection method as a supervised learning approach.
The paper is organized in five sections. Technology backgrounds of our approach are presented in Section
Given a training dataset
Suppose that we define a matrix by putting
How to get the close solution of the sparse representation problem is NPhard, because it is a combinational optimization. If we replace the
Recently, development in the theory of compressed sensing and sparse representation reveals that, if the solution of (
We can solve the problem in polynomial time by quadratic programming or standard linear programming methods. If the solution is very sparse, there will be more efficient methods to solve this problem.
Twin support vector machines (TWSVMs) are a new binary data classifier proposed by Jayadeva et al. [
According to (
(TWSVM1)
(TWSVM2)
The first term, in the objective function of (
TWSVMs are composed of two QPPs. And the objective function in each QPP, corresponding to a particular class and constrains, is determined by the patterns belonging to the other class. In TWSVM1, patterns of class +1 are clustered near the hyper plane
If we get the vector
From the K.K.T. conditions, we can observe that patterns lie on the hyper plane given by
An example of SVMs and TWSVMs:
The digital database for screening mammography (DDSM) [
To summarize quantitatively the performance of the proposed method, we used receiver operating characteristic (ROC) curves [
Ideally, the nonzero entries in the estimated
To better model the structure, we classify
Input: We have a matrix of training images
Compute features
Solve the convex optimization problem:
Compute the residuals
Output:
Given a set of mammogram blocks, each block is transformed and represented in terms of the sparse coefficients with respect to the parts from the vocabulary constructed in the image sparse representation and learning stage. Each block is then transformed into a vector and represented as a sparse feature vector based on the vocabulary parts (the negative and positive samples in the sparse learning set). Then we can use the learned sparse coefficients as each block’s sparse feature. So we consider the sparse representation approach as a feature extraction method in terms of the coefficient vector, and then we feed it with the stateoftheart classifier (TWSVMs) to formulate the detection method as a supervised learning approach.
If we have a set of training blocks labeled as positive (MCs) or negative (nonMCs), each image is represented as a feature vector using the method described above. These feature vectors are then fed as inputs to TWSVMs, which learns to classify an image block as a member or not a member of the object category, under some associated confidence. When we get the learned TWSVMs model, we can use the learned classifier as a reliable detector to perform the detection task.
Up till now, we have illustrated our new methods to detect MCs in mammograms. In this section, we will evaluate the performance of our methods by using the real mammogram data obtained from DDSM. In our experiments, we use the training, test, and validation sets, which were randomly selected from the preprocessed image blocks. The blocks included 3000 with true MCs and 3000 with normal tissue. We chose 75% of the blocks for training and 25% for test.
For a given digital mammogram, we formulate the MCs detection and classification approach as the following steps.
We first preprocess the mammogram to remove the artifacts, suppress inhomogeneity of the image background, and enhance microcalcifications in the breast area.
At each pixel location of the image, we manually select a small window (
Get the sparse representation of each image block by using the proposed methods.
Apply the proposed MCs detection methods to decide whether
In our experiments, they are designed to quantitatively verify the performance of sparse representation based methods for MCs detection and classification by using mammograms. To get an accurate performance measure in this study, a stratified 5fold cross validation method is employed. We also compared our approaches with the stateoftheart algorithm, SVMs, which have been successfully applied in MCs detection.
All the experiments are performed on a notebook computer with DUO Intel 2.54 G CPU and 4 G memory under Windows 7. MATLAB 2011 is used to implement sparse representation based MCs detection methods. To get the sparse representation of each image block, we employed the
Before we performed the MCs detection methods, we first used the
First, we did the experiments using MCsSRC algorithm to perform the MCs detection and classification. The test results are summarized with ROC curves in Figure
Comparisons of ROC curves of MCs detection and classification using the proposed methods.
From Figure
To evaluate the stability of our methods, we repeat the sampling 50 times so that we can compute the mean and standard deviation of the detection accuracy, sensitivity, and specificity. We perform the detection and classification task in 20 rounds, and in each round we randomly select training samples from 95% of training samples to 5% to train classifiers. The trained classifiers are evaluated using the other 500 test samples. Average experimental results of the MCsSRC method, compared with SVMs and TWSVMs, are shown in Table
Experimental results of the proposed MCsSRC method for MCs detection, compared with sparse representation based TWSVMs and SVMs methods.
Methods  Sensitivity  Specificity  Az 

MCsSRC 



TWSVMsSR 



SVMsSR 



From Table
In this paper, a novel approach is described to aid breast cancer detection and classification using digital mammograms. The proposed method is based on sparse feature learning and representation, which expresses a testing sample as a linear combination of the built vocabulary (training samples). The sparse coefficient vector is obtained by using
The author declares that there is no conflict of interests regarding the publication of this paper.
The author in this paper would like thank Shaanxi Provincial Education Department. All the work presented is supported by the key discipline of Shaanxi Province and the Scientific Research Program funded by Program no. 12JK0741. The author is also very grateful to the editor and anonymous reviewers who made their kind constructive comments and suggestions.