MG-SpaIR: Multi-Grade Sparse-Guided Implicit Representation for Training-Data-Free Image Restoration

Area of Science:

• Computer Vision
• Image Processing
• Machine Learning

Background:

• Image restoration is crucial for recovering high-quality images from various degradations.
• Existing methods often rely on large training datasets, limiting their applicability.
• Implicit Neural Representations (INRs) offer a promising data-free approach but face challenges with fidelity and artifacts.

Purpose of the Study:

• To develop a training-data-free image restoration framework capable of handling mixed degradations.
• To improve the representational fidelity and spectral limitations of INRs.
• To stabilize INR optimization and suppress artifacts for robust image reconstruction.

Main Methods:

• Introduced MG-SpaIR, a framework leveraging Implicit Neural Representations (INRs).
• Proposed a multi-grade residual hierarchy for progressive refinement from low to high spatial frequencies.
• Incorporated explicit sparse proximal regularization (e.g., $\ell_0$ type) in the high-resolution domain to preserve structures and suppress artifacts.
• Employed a multi-grade proximal alternating scheme for efficient optimization with convergence guarantees.

Main Results:

• MG-SpaIR demonstrated superior performance on mixed-degradation benchmarks compared to training-data-free baselines.
• The multi-grade hierarchy effectively improved representational fidelity and addressed spectral limitations.
• Sparse regularization successfully stabilized optimization and mitigated INR-induced artifacts while preserving sharp image structures.

Conclusions:

• MG-SpaIR offers a stable, interpretable, and data-efficient alternative for image restoration.
• The proposed framework advances training-data-free methods for complex image restoration tasks.
• This approach shows significant potential for applications where training data is scarce or unavailable.