Sparsity-driven regularization has undergone significant development in single-image restoration, particularly with the transition from handcrafted priors to trainable deep architectures. In this work, a geometric prior-enhanced deep image prior (DIP) framework, termed DIP-MC, is proposed that integrates mean curvature (MC) regularization to promote natural smoothness and structural coherence in reconstructed images. To strengthen the representational capacity of DIP, a self-attention module is incorporated between the encoder and decoder, enabling the network to capture long-range dependencies and preserve fine-scale textures. In contrast to total variation (TV), which frequently produces piecewise-constant artifacts and staircasing, MC regularization leverages curvature information, resulting in smoother transitions while maintaining sharp structural boundaries. DIP-MC is evaluated on standard grayscale and color image denoising and deblurring tasks using benchmark datasets including BSD68, Classic5, LIVE1, Set5, Set12, Set14, and the Levin dataset. Quantitative performance is assessed using peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) metrics. Experimental results demonstrate that DIP-MC consistently outperformed the DIP-TV baseline with 26.49 PSNR and 0.9 SSIM. It achieved competitive performance relative to BM3D and EPLL models with 28.6 PSNR and 0.87 SSIM while producing visually more natural reconstructions with improved detail fidelity. Furthermore, the learning dynamics of DIP-MC are analyzed by examining update-cost behavior during optimization, visualizing the best-performing network weights, and monitoring PSNR and SSIM progression across training epochs. These evaluations indicate that DIP-MC exhibits superior stability and convergence characteristics. Overall, DIP-MC establishes itself as a robust, scalable, and geometrically informed framework for high-quality single-image restoration.
Israr et al. (Sat,) studied this question.