Deformable Sparse-Gradient Regularization for Extreme Image Denoising

Extreme noise severely degrades image quality in photon-limited imaging systems and challenges existing denoising methods. Classical total variation (TV) models rely on fixed local gradients and often introduce cross-edge smoothing, while deep learning methods may become unstable under extremely low signal-to-noise ratios. To address these limitations, we propose DSGR-Net, a hybrid denoising framework integrating Deformable Sparse-Gradient Regularization (DSGR) preprocessing with neural network restoration. The proposed DSGR model performs adaptive neighborhood regularization by selecting the eight smallest local gradients within a deformable neighborhood for sparse total variation compensation. This structure-aware strategy effectively suppresses noise while avoiding cross-edge diffusion and preserving fine image details. Experimental results on both simulated and real optical imaging data demonstrate that the proposed DSGR-Net achieves improved structural preservation and noise suppression compared with representative denoising methods.