Selection of regularization parameter for optical topography.

Area of Science:

• Computational physics
• Image processing
• Optical engineering

Background:

• Ill-posed inverse problems, such as those in optical topography and deblurring, are sensitive to the choice of regularization parameters.
• Accurate solutions require careful selection of regularization parameters to balance data fidelity and solution smoothness.

Purpose of the Study:

• To review and evaluate eleven distinct methods for selecting the Tikhonov regularization parameter.
• To determine the most effective method for parameter selection in optical topography and deblurring.

Main Methods:

• A comprehensive literature review of eleven Tikhonov regularization parameter selection methods.
• Empirical testing of these methods on two benchmark problems: image deblurring and optical topography reconstruction.

Main Results:

• The L-curve method demonstrated superior performance and reliability across the tested problems.
• Generalized cross-validation (GCV) showed promise as an alternative, particularly for severely ill-posed problems.

Conclusions:

• The L-curve method is identified as the preferred approach for Tikhonov regularization parameter selection in optical topography.
• Generalized cross-validation offers a valuable alternative when dealing with particularly ill-posed inverse problems.