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中文摘要：
医学颅脑图像处理已成为脑部疾病诊断的重要途径，为去除颅脑图像的噪声和异物遮挡而又不损失正常组织信息，提出了一种基于L1范数鲁棒主成分分析降维的颅脑图像恢复方法。首先用L1范数代替传统主成分分析中的L2范数，构造对噪声更加鲁棒的Ll范数主成分分析；然后对其代价函数进行交替凸规划算法计算图像降维后的特征数据与投影矩阵；最后利用线性变换得到恢复后的医学颅脑图像。与传统图像压缩与恢复方法不同，该方法利用了L1范数的噪声鲁棒性，通过降维的方法来实现颅脑图像的恢复，同时实现去噪和异常检测的功能。在真实颅脑图像库中进行的比较实验证明了该方法对于颅脑图像恢复的有效性。
英文摘要：
As medical cerebral images have become an effective way of brain disease diagnosis, an efficient medical cerebral images recov- ery method based on LI norm robust PCA dimensionality reduction is proposed to achieve denoising and anomaly detection with no loss of normal tissue information. First the L1 norm principal component analysis is constructed using L1 norm which is more robust to noise while in traditional principal component analysis it uses L2 norm. Then the characteristic data and the projection matrix are gotten by the alternate convex programming algorithm of the cost function. Finally, medical cerebral images after recovery are obtained by the linear transformation. Different from the traditional image compression and recovery method, the proposed method makes use of the robustness of the L1 norm. It realizes medical brain images recovery by dimension reduction, at the same time achieves denoising and anomaly detec- tion. The experimental results compared with the standard PCA algorithm in the real cerebral image database also prove the effectiveness of the proposed method for cerebral images recovery.
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