This article proposes a new dimension reduction algorithm based on low-dimensional ordered orthogonal projection, which is used for cancer detection with terahertz (THz) images of freshly excised human breast cancer tissues. A THz image can be represented by a data cube with each pixel containing a high-dimensional spectrum vector covering several THz frequencies, where each frequency represents a different dimension in the vector. The proposed algorithm projects the high-dimensional spectrum vector of each pixel within the THz image into a low-dimensional subspace that contains the majority of the unique features embedded in the image. The low-dimensional subspace is constructed by sequentially identifying its orthonormal basis vectors, such that each newly chosen basis vector represents the most unique information not contained by existing basis vectors. A multivariate Gaussian mixture model is used to represent the statistical distributions of the low-dimensional feature vectors obtained from the proposed dimension reduction algorithm. The model parameters are iteratively learned by using unsupervised learning methods, such as Markov chain Monte Carlo or expectation maximization, and the results are used to classify the various regions within a tumor sample. Experiment results demonstrate that the proposed method achieves apparent performance improvement in human breast cancer tissue over existing approaches such as one-dimensional Markov chain Monte Carlo. The results confirm that the dimension reduction algorithm presented in this article is a promising technique for breast cancer detection with THz images, and the classification results present a good correlation with respect to the histopathology results of the analyzed samples.

中文翻译：

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太赫兹成像中低维有序正交投影的乳腺癌检测


本文提出了一种基于低维有序正交投影的新降维算法，用于利用新鲜切除的人类乳腺癌组织的太赫兹（THz）图像进行癌症检测。太赫兹图像可以用数据立方体表示，其中每个像素包含覆盖多个太赫兹频率的高维频谱向量，其中每个频率代表向量中的不同维度。所提出的算法将太赫兹图像内每个像素的高维频谱矢量投影到包含图像中嵌入的大部分独特特征的低维子空间中。低维子空间是通过顺序识别其正交基向量来构造的，使得每个新选择的基向量代表现有基向量不包含的最独特的信息。使用多元高斯混合模型来表示从所提出的降维算法获得的低维特征向量的统计分布。通过使用无监督学习方法（例如马尔可夫链蒙特卡罗或期望最大化）迭代学习模型参数，并将结果用于对肿瘤样本内的各个区域进行分类。实验结果表明，与一维马尔可夫链蒙特卡罗等现有方法相比，该方法在人类乳腺癌组织中实现了明显的性能改进。结果证实，本文提出的降维算法是一种很有前途的太赫兹图像乳腺癌检测技术，并且分类结果与分析样本的组织病理学结果具有良好的相关性。