Dept. of Electr. and Comput. Eng., Illinois Inst. of Technol., Chicago, IL.
IEEE Trans Image Process. 1992;1(3):322-36. doi: 10.1109/83.148606.
The application of regularization to ill-conditioned problems necessitates the choice of a regularization parameter which trades fidelity to the data with smoothness of the solution. The value of the regularization parameter depends on the variance of the noise in the data. The problem of choosing the regularization parameter and estimating the noise variance in image restoration is examined. An error analysis based on an objective mean-square-error (MSE) criterion is used to motivate regularization. Two approaches for choosing the regularization parameter and estimating the noise variance are proposed. The proposed and existing methods are compared and their relationship to linear minimum-mean-square-error filtering is examined. Experiments are presented that verify the theoretical results.
正则化在病态问题中的应用需要选择一个正则化参数，该参数在数据的保真度和解的平滑度之间进行权衡。正则化参数的值取决于数据中噪声的方差。本文研究了在图像恢复中选择正则化参数和估计噪声方差的问题。基于客观均方误差（MSE）准则的误差分析用于正则化的动机。提出了两种选择正则化参数和估计噪声方差的方法。比较了所提出的方法和现有的方法，并研究了它们与线性最小均方误差滤波的关系。实验验证了理论结果。
