Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation

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. In this paper 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 new approaches for choosing the regularization parameter and estimating the noise variance are proposed. The proposed and existing methods are compared and their relation to linear minimum mean square error (LMMSE) filtering is examined. Experiments are presented that verify the theoretical results.