图 书 馆
面片复杂度、有限像素相关性与最优去噪Patch Complexity, Finite Pixel Correlations and Optimal Denoising |
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| 课程网址: | http://videolectures.net/eccv2012_levin_denoising/ |
| 主讲教师: | Anat Levin |
| 开课单位: | 魏茨曼科学研究所 |
| 开课时间: | 2012-11-12 |
| 课程语种: | 英语 |
| 中文简介: |  图像恢复任务是不适的问题，通常可以通过先验解决。由于最佳先验是自然图像的确切未知密度，因此实际先验仅是近似值，通常仅限于小块。这就提出了几个问题：我们希望通过未来的复杂算法在多大程度上改善当前的恢复结果？从根本上说，即使对自然图像统计数据拥有完备的知识，问题的内在含混性又是什么？另外，由于大多数当前方法仅限于有限支持补丁或内核，自然图像的补丁复杂性，补丁大小和恢复错误之间有什么关系？专注于图像去噪，我们做出了一些贡献。首先，鉴于计算限制，我们以非参数方法研究了降噪增益与样本大小要求之间的关系。我们提出了收益递减的规律，即随着补丁大小的增加，稀有补丁不仅需要更大的数据集，而且从中获取的收益也很少。该结果表明了用于降噪的新颖的自适应可变大小补丁方案。其次，我们研究了绝对降噪极限，而与所使用的算法无关，并且它们的收敛速度是斑片大小的函数。自然图像的尺度不变性在这里起着关键作用，既意味着去噪上严格的正下界，又意味着幂定律收敛。外推此参数定律可对最佳可实现的降噪进行粗略估计，这表明尽管有适度的改进，还是有可能的。 |
| 课程简介: | Image restoration tasks are ill-posed problems, typically solved with priors. Since the optimal prior is the exact unknown density of natural images, actual priors are only approximate and typically restricted to small patches. This raises several questions: How much may we hope to improve current restoration results with future sophisticated algorithms? And more fundamentally, even with perfect knowledge of natural image statistics, what is the inherent ambiguity of the problem? In addition, since most current methods are limited to finite support patches or kernels, what is the relation between the patch complexity of natural images, patch size, and restoration errors? Focusing on image denoising, we make several contributions. First, in light of computational constraints, we study the relation between denoising gain and sample size requirements in a non parametric approach. We present a law of diminishing return, namely that with increasing patch size, rare patches not only require a much larger dataset, but also gain little from it. This result suggests novel adaptive variable-sized patch schemes for denoising. Second, we study absolute denoising limits, regardless of the algorithm used, and the converge rate to them as a function of patch size. Scale invariance of natural images plays a key role here and implies both a strictly positive lower bound on denoising and a power law convergence. Extrapolating this parametric law gives a ballpark estimate of the best achievable denoising, suggesting that some improvement, although modest, is still possible. |
| 关 键 词: | 图像恢复; 数据集 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2021-04-07：zyk |
| 最后编审: | 2021-04-07：zyk |
| 阅读次数: | 48 |