MG-SpaIR: Multi-grade Sparse-guided Implicit Representation for Training-Data-Free Image Restoration
This work provides a stable, interpretable, and data-efficient alternative to learning-based methods for single-image restoration under complex degradations, though it is incremental as it builds on existing INR and sparse regularization techniques.
MG-SpaIR introduces a training-data-free framework for image restoration from mixed degradations (blur, downsampling, noise, missing pixels) using a multi-grade coarse-to-fine residual hierarchy with explicit sparse regularization, achieving consistent improvements over Deep Image Prior on mixed-degradation benchmarks.
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., $\ell_0$-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.