Convergence of SC-RCCTV with adaptive noise-level updates

Establish convergence of the SC-RCCTV alternating direction method of multipliers iteration when the band-wise noise levels and corresponding weights are adaptively updated during the iterations.

Background

The SC-RCCTV algorithm alternates between restoration updates and online refinement of the band-wise Gaussian noise estimates. Because these adaptive updates change the weights during the iterations, standard convergence results for ADMM do not directly apply. Although the authors consistently observe stable behavior in experiments and report that the estimated noise levels have nearly settled at termination, a convergence guarantee for the resulting adaptive iteration is not established.

References

The two classes of methods are therefore complementary. Several aspects of the model deserve further study: the rank-8 spatial representation limits the recovery of near-dead bands; the line-constant stripe model does not capture stripes that cover only part of a line, and it cannot always distinguish stripes from image structures that are themselves nearly constant along a line, such as straight roads or field boundaries; and the convergence of the iteration with adaptive noise levels, although consistently observed, remains to be proven.

— Self-Calibrated Subspace Robust PCA for Parameter-Free Removal of Mixed Noise and Line Stripes in Hyperspectral Images  (2610.21896 - Wang, 15 Oct 2026) in Section 5.4, “Applicability and Limitations”