Explore alternative sparsifying transforms and develop fast EBF solvers

Develop and evaluate empirical Bayes framework algorithms that use sparsifying transforms beyond the discrete cosine transform (DCT), and construct fast solvers tailored to these bases to improve image restoration quality.

Background

The numerical experiments in the paper focus on image deblurring using DCT as the sparsifying transform, leveraging its diagonalization properties for efficient computation and demonstrating how appropriate hyperpriors enhance sparsity and restoration accuracy.

To further improve performance and broaden applicability, exploring alternative transforms (e.g., wavelets, learned dictionaries) and designing fast solvers compatible with these bases within the empirical Bayes framework is identified as an open direction.

References

Several directions remain open for future work. Finally, to further improve image restoration quality, we will explore alternative sparsifying transforms beyond DCT, and develop fast solvers tailored to these bases within EBF.

— Sparsity via Hyperpriors: A Theoretical and Algorithmic Study under Empirical Bayes Framework (2511.06235 - Li et al., 9 Nov 2025) in Section 6 (Conclusions)