Image Interpolation Via Regularized Local Linear Regression
Image Interpolation Via Regularized Local Linear Regression
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DOI：
10.1109/pcs.2010.5702437
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发表时间：
2010-12
影响因子：
10.6
通讯作者：
Xianming Liu;Debin Zhao;Ruiqin Xiong;Siwei Ma;Wen Gao
中科院分区：
文献类型：
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作者：
Xianming Liu;Debin Zhao;Ruiqin Xiong;Siwei Ma;Wen Gao
线性回归模型是设计有效图像插值方案的一个非常有吸引力的工具。文献中已经提出了一些基于回归的图像插值算法，其中目标函数采用普通最小二乘（OLS）优化。然而，它表明，插值与OLS可能有一些不可取的属性从鲁棒性的角度来看：即使是少量的离群值可以显着影响估计。针对这些问题，本文提出了一种基于正则化局部线性回归（RLLR）的图像插值算法。从线性回归模型开始，我们用移动最小二乘（MLS）误差范数替换OLS误差范数，从而得到局部图像结构的鲁棒估计。为了保持解的稳定性并避免过拟合，我们将N2-范数作为估计器复杂性惩罚。此外，基于流形的半监督学习的最新进展的动机，我们明确考虑的内在流形结构，利用测量和未测量的数据点。具体来说，我们的框架采用了几何结构的边缘概率分布引起的未测量的样本作为一个额外的本地平滑保持约束。通过求解一个凸优化问题，可以得到最优模型参数的封闭解。基准测试图像上的实验结果表明，该方法实现了非常有竞争力的性能与国家的最先进的插值算法，特别是在图像边缘结构的保护。
The linear regression model is a very attractive tool to design effective image interpolation schemes. Some regression-based image interpolation algorithms have been proposed in the literature, in which the objective functions are optimized by ordinary least squares (OLS). However, it is shown that interpolation with OLS may have some undesirable properties from a robustness point of view: even small amounts of outliers can dramatically affect the estimates. To address these issues, in this paper we propose a novel image interpolation algorithm based on regularized local linear regression (RLLR). Starting with the linear regression model where we replace the OLS error norm with the moving least squares (MLS) error norm leads to a robust estimator of local image structure. To keep the solution stable and avoid overfitting, we incorporate the ℓ2-norm as the estimator complexity penalty. Moreover, motivated by recent progress on manifold-based semi-supervised learning, we explicitly consider the intrinsic manifold structure by making use of both measured and unmeasured data points. Specifically, our framework incorporates the geometric structure of the marginal probability distribution induced by unmeasured samples as an additional local smoothness preserving constraint. The optimal model parameters can be obtained with a closed-form solution by solving a convex optimization problem. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance with the state-of-the-art interpolation algorithms, especially in image edge structure preservation.