| 基于矩阵变换的图像置乱逆问题求解 |
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| 引用本文： | 邵利平,覃征,衡星辰,高洪江.基于矩阵变换的图像置乱逆问题求解[J].电子学报,2008,36(7):1355-1363. |
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| 作者姓名： | 邵利平 覃征 衡星辰 高洪江 |
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| 作者单位： | 西安交通大学电子商务研究所,陕西西安,710049;西安交通大学电子商务研究所,陕西西安,710049;清华大学软件学院,北京,100084;西安交通大学电子商务研究所,陕西西安,710049;鲁东大学计算机科学与技术学院,山东烟台,264025 |
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| 基金项目： | 国家重点基础研究发展计划(973计划)，国防科技预研项目 |
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| 摘 要： | 基于矩阵变换的图像置乱用周期性对图像恢复,代价高昂;而通过逆变换恢复,已有方法未解决 Z N上逆阵求解问题.针对此问题,通过构造映射规则,将伴随矩阵求逆方法推广到 Z N,解决了n维矩阵变换的逆问题.为减小该方法计算代价,将杜里特尔分解和克劳特分解求逆推广到 Z N,解决了变换阵顺阶主子式模N互质,矩阵变换的逆问题.为弱化扩展杜里特尔分解和克劳特分解求逆条件,将高斯-约当消去法推广到 Z N,给出了任意变换阵在 Z N上求逆算法和简化求逆算法.所提方法可用于得到任意变换阵在 Z N上的逆变换阵,从而可直接对图像恢复,而不必计算可恢复周期.实验表明所提方法的可行性和有效性.
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| 关 键 词： | 图像置乱变换 杜里特尔分解 克劳特分解 高斯-约当消去 逆变换 乘法逆元 |
| 收稿时间： | 2007-05-15 |
Solution for the Inverse Problem of Matrix Transform Based Image Scrambling |
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| SHAO Li-ping,QIN Zheng,HENG Xing-chen,GAO Hong-jiang.Solution for the Inverse Problem of Matrix Transform Based Image Scrambling[J].Acta Electronica Sinica,2008,36(7):1355-1363. |
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| Authors: | SHAO Li-ping QIN Zheng HENG Xing-chen GAO Hong-jiang |
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| Institution: | SHAO Li-ping1,QIN Zheng1,2,HENG Xing-chen1,GAO Hong-jiang1,3(1.Research Institute of Electronic Commerce,Xi\'an Jiaotong University,Xi\'an,Shaanxi 710049,China,2.School of Software,Tsinghua University,Beijing 100084,3.School of Computer Science , Technology,Ludong University,Yantai,Sh,ong 264025,China) |
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| Abstract: | In matrix transform based image scrambling,the cost to restore image by periodicity is expensive.To restore image by inverse mapping,existing methods do not solve the problem computing inverse matrix in ZN.To address it,this paper expanded the method getting inverse matrix by adjoint matrix to ZN through constructing mapping regulations.To decrease the expensive cost of it,this paper generalized Doolittle decomposition and Crout decomposition into ZN,which solves the inverse problem of any n dimensional mat... |
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| Keywords: | image scrambling transform Doolittle decomposition Crout decomposition Gauss-Jordan elimination inverse transform multiplication inversion |
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