Jun 30, 2026cs.CV
MG-SpaIR is a training-data-free framework for restoring a clean image from a single observation corrupted by a mixture of blur, downsampling, noise, and missing pixels. Building on implicit neural representations (INRs), we introduce a multi-grade coarse-to-fine residual hierarchy that progressively refines the reconstruction across resolution grades, improving representational fidelity and mitigating spectral limitations. To stabilize reconstruction optimization and suppress INR-induced artifacts, we further propose an explicit sparse proximal regularization (e.g.,
ℓ0-type) applied directly in the high-resolution image domain, which discourages spurious high-frequency patterns while preserving sharp structures. The resulting optimization is solved efficiently via a multi-grade proximal alternating scheme, and we establish convergence guarantees for the associated updates under standard regularity conditions. Experiments on mixed-degradation benchmarks demonstrate that MG-SpaIR consistently outperforms strong training-data-free baselines such as Deep Image Prior, providing a stable, interpretable, and data-efficient alternative to conventional learning-based restoration methods.
Jianmin Liao, Lei Huang, Ronglong Fang +3
Department of Mathematics, Syracuse University, 215 Carnegie Building, Syracuse, 13210, NY, USA. · Department of Mathematics & Statistics, Old Dominion University, 2300 Engineering & Computational Sciences Building, Norfolk, 23529, VA, USA. · Department of Medical Physical, Memorial Sloan Kettering Cancer Center, 1250 First Avenue, New York, 10065, NY, USA. +1