Adaptive randomized SVD rank selection

Develop an adaptive randomized singular value decomposition approach that suitably chooses the retained rank for a given observational noise level in order to balance truncation-induced undercoverage against variance-induced overcoverage in pixelwise confidence intervals for Landweber reconstructions.

Background

The numerical experiments show a trade-off between the randomized SVD rank and confidence-interval coverage. At low noise levels, retaining too few singular directions can omit important components and cause undercoverage, whereas at higher noise levels, retaining many small-singular-value directions can excessively inflate the propagated uncertainty and produce overcoverage.

Because the appropriate rank appears to depend on the observational noise level, the paper identifies adaptive rank selection as an unresolved methodological problem for making the randomized-SVD-based uncertainty quantification procedure reliably attain nominal coverage across noise regimes.

References

This suggests the need to develop an adaptive randomized SVD approach to suitably choose a rank for a given noise level. We leave this to be addressed in a future work.

— Uncertainty Quantification for Landweber Iteration with Randomized Normal-Operator Approximation  (2610.00882 - Abhishek et al., 1 Oct 2026) in Section 4, subsection “Simulation results and interpretation”