This project proposes a new dimension reduction algorithm based on low-dimension ordered orthogonal projection (LOOP), 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 dimension spectrum vector covering several THz frequencies, where each frequency represents a different dimension in the vector. The proposed algorithm projects the high-dimension spectrum vector of each pixel within the THz image into a low dimension subspace that contains the majority of the unique features embedded in the image. The low dimension 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 dimension 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- dimension Markov chain Monte Carlo. The results confirm that the dimension reduction algorithm presented in this paper 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. This project is implemented with MATLAB software.

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