Search Results (2)

To address the challenges of image inpainting in scenarios with extensive or irregular missing regions—particularly detail oversmoothing, structural ambiguity, and textural incoherence—this paper proposes an Image Structure-Guided (ISG) framework that hierarchically integrates structural priors with semantic-aware texture synthesis. The proposed methodology advances a two-stage restoration paradigm: (1) Structural Prior Extraction, where adaptive edge detection algorithms identify residual contours in corrupted regions, and a transformer-enhanced network reconstructs globally consistent structural maps through contextual feature propagation; (2) Structure-Constrained Texture Synthesis, wherein a multi-scale generator with hybrid dilated convolutions and channel attention mechanisms iteratively refines high-fidelity textures under explicit structural guidance. The framework introduces three innovations: (1) a hierarchical feature fusion architecture that synergizes multi-scale receptive fields with spatial-channel attention to preserve long-range dependencies and local details simultaneously; (2) spectral-normalized Markovian discriminator with gradient-penalty regularization, enabling adversarial training stability while enforcing patch-level structural consistency; and (3) dual-branch loss formulation combining perceptual similarity metrics with edge-aware constraints to align synthesized content with both semantic coherence and geometric fidelity. Our experiments on the two benchmark datasets (Places2 and CelebA) have demonstrated that our framework achieves more unified textures and structures, bringing the restored images closer to their original semantic content. Full article

This paper deals with the Tikhonov regularization for nonlinear ill-posed operator equations in Hilbert scales with oversmoothing penalties. One focus is on the application of the discrepancy principle for choosing the regularization parameter and its consequences. Numerical case studies are performed in order to complement analytical results concerning the oversmoothing situation. For example, case studies are presented for exact solutions of Hölder type smoothness with a low Hölder exponent. Moreover, the regularization parameter choice using the discrepancy principle, for which rate results are proven in the oversmoothing case in in reference (Hofmann, B.; Mathé, P. Inverse Probl. 2018, 34, 015007) is compared to Hölder type a priori choices. On the other hand, well-known analytical results on the existence and convergence of regularized solutions are summarized and partially augmented. In particular, a sketch for a novel proof to derive Hölder convergence rates in the case of oversmoothing penalties is given, extending ideas from in reference (Hofmann, B.; Plato, R. ETNA. 2020, 93). Full article