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<p>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 residual hierarchy that progressively refines the reconstruction from low to high spatial frequencies across 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., <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell _0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月30日

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  • Jianmin Liao,
  • Lei Huang,
  • Ronglong Fang,
  • Ashley Prater-Bennette,
  • Lixin Shen,
  • Yuesheng Xu

摘要

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 residual hierarchy that progressively refines the reconstruction from low to high spatial frequencies across 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., \(\ell _0\) ℓ 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.