Downward Continuation Iterative Regularization Solution Based on Quasi⁃Optimal Regularization Factor Set

Objectives This paper addresses a critical limitation hindering the practical application of widely used iterative regularization methods, such as Tikhonov regularization and Landweber regularization. The lack of a clear strategy for optimally pairing iteration counts with regularization parameters.

Methods The concept of a quasi-optimal regularization factor set is constructed. By analyzing the distribution of iteration counts and regularization parameters within these sets, a strategy for selecting the best regularization factor group is proposed. Furthermore, a formula is presented to determine the optimal regularization parameter corresponding to a given iteration count using the L-curve method.

Results Analysis of the extension error and the variation within quasi-optimal factor sets reveals a significant correlation between optimal regularization parameters and iteration counts. When the iteration count exceeds 10, the extension solutions corresponding to different quasi-optimal factor sets become nearly identical. For sufficiently large iteration counts, any quasi-optimal factor set yields similar effects. Compared with the traditional Tikhonov regularization, the proposed iterative method based on the new selection strategy produces smoother extension solutions with smaller errors. However, in regions with sharp data variations, some high-frequency signals may be filtered out as noise, leading to no significant improvement in extension performance there.

Conclusions The proposed iterative regularization algorithm incorporates the novel selection strategy,and generates smoother and more accurate extension solutions than the traditional Tikhonov method.The results demonstrate its reliability and practical utility.