Locally Linear Denoising on Image Manifolds
Locally Linear Denoising on Image Manifolds
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发表时间：
2010-03
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通讯作者：
Dian Gong;Fei Sha;G. Medioni
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作者：
Dian Gong;Fei Sha;G. Medioni
我们研究图像去噪问题，其中图像被假设为来自低维（子）流形的样本。我们提出了局部线性去噪算法。该算法通过构造最近邻图来近似具有局部线性补丁的流形。然后，每个图像在其邻域内进行局部去噪。然后通过对齐这些局部估计来确定全局最佳去噪结果。该算法具有计算效率高的封闭式解。我们在两个图像数据集上对该算法与替代方法进行了评估和比较。我们证明了所提出算法的有效性，该算法产生了视觉上吸引人的去噪结果，当去噪数据用于监督学习任务时，会产生较小的重建误差并导致较低的错误率。
We study the problem of image denoising where images are assumed to be samples from low dimensional (sub)manifolds. We propose the algorithm of locally linear denoising. The algorithm approximates manifolds with locally linear patches by constructing nearest neighbor graphs. Each image is then locally denoised within its neighborhoods. A global optimal denoising result is then identified by aligning those local estimates. The algorithm has a closed-form solution that is efficient to compute. We evaluated and compared the algorithm to alternative methods on two image data sets. We demonstrated the effectiveness of the proposed algorithm, which yields visually appealing denoising results, incurs smaller reconstruction errors and results in lower error rates when the denoised data are used in supervised learning tasks.