Hierarchical sparse Bayesian learning with adaptive Laplacian prior for single image super-resolution

Single-image super-resolution (SISR) continues to face difficulties in reconstructing perceptually critical details from degraded low-resolution observations. While conventional Bayesian approaches utilizing Relevance Vector Machines (RVMs) provide probabilistic interpretations, their reliance on fixed blur kernel definitions and homogeneous pixel dependency models often yields artifacts in complex scenarios. To resolve these issues, this study introduces a hierarchical Bayesian architecture enhanced by an adaptive Laplacian prior, which extends the sparse Bayesian learning (SBL) paradigm. Diverging from traditional Gaussian-based frameworks, our method employs sparsity-inducing regularization to selectively prioritize structurally salient regions (e.g., edge discontinuities, texture boundaries), while dynamically quantifying reconstruction uncertainty through pixel-wise variance analysis. Additionally, a spatially adaptive optimization mechanism is designed to streamline computational workflows without compromising restoration fidelity. Evaluations across multiple benchmarks confirm the framework's advantages: it surpasses existing state-of-the-art techniques in both quantitative metrics (PSNR, SSIM) and qualitative assessments, demonstrating superior artifact suppression in high-frequency domains. Comparative analyses against recent state-of-the-art models further validate its capability to harmonize sparse representation with structural coherence.