三种常见的正则化图像处理模型研究
Research on Three Common Regularized Image Processing Models
DOI: 10.12677/AAM.2018.75074, PDF,    科研立项经费支持
作者: 童蓓蕾：中国科学技术大学，数学学院，安徽 合肥 ；常谦顺：中国科学院，数学与系统科学研究院，北京
关键词: 全变分；图像处理；图像去噪；Tikhonov正则；L0-平滑；Bregman迭代；Total Variation； Image Processing； Image Denoising； Tikhonov Regularization； L0-Smoothing； Bregman Iteration
摘要: 正则化是反问题中的一个重要课题，恰当地选取正则化项对于反问题的求解至关重要。图像复原是一个典型的反问题，因此正则化项的探讨对于图像复原也非常必要。介绍了Tikhonov正则、全变分正则及梯度的L0正则等三种正则化模型，分别给出算例对灰度图和RGB图进行了复原处理。发现Tikhonov正则化去噪时会产生模糊；全变分正则化去噪能较好地保持边界；而L0正则化平滑方法对噪音比较敏感。
Abstract: Regularization is an important topic in inverse problems. Proper selection of regularization terms is essential for solving inverse problems. Image restoration is a typical inverse problem, so the discussion of regularization is also necessary for image restoration. Three regularization models, Tikhonov regularization, total variation regularization and gradient L0 regularization are intro-duced. Examples are given to restore grayscale and RGB images. It is found that denoising with Tikhonov regularization can produce blurring, while denoising with total variation regularization can preserve the boundary and the detail information; however, the L0 regularization smoothing is more sensitive to noise.
文章引用：童蓓蕾, 常谦顺. 三种常见的正则化图像处理模型研究[J]. 应用数学进展, 2018, 7(5): 622-631. https://doi.org/10.12677/AAM.2018.75074

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