Joint Non-Local Statistical and Wavelet Tight Frame Information-Based ℓ₀ Regularization Model for Image Deblurring

The task of image deblurring is a complex and ill-posed inverse problem, which endeavors to restore a high-fidelity image from its degraded and blurred counterpart. Traditional deblurring methodologies are often confronted with the challenge of maintaining the integrity of image details and edges throughout the restoration procedure. This paper delves into an innovative approach that synergistically harnesses the power of non-local statistical properties and wavelet tight frame based $\ell _{0}$ regularization. The presented model integrates non-local statistical priors pertaining to the image in question into its regularization framework. Meanwhile, it leverages the robustness of wavelet tight frames to counteract the inherent ill-posedness of image deblurring scenarios. This dual strategy results in a more effective preservation of fine details and edges during the deblurring process. Empirical numerical simulations corroborate the efficacy of the presented algorithm. It demonstrates a marked superiority over existing deblurring techniques in terms of quantitative metrics such as Peak Signal-to-Noise Ratio (PSNR), Root Mean Square Error (RMSE), Structural Similarity Index (SSIM), and Universal Image Quality Index (UQI). Consequently, the presented algorithm yields images of enhanced deblurring quality, substantiating its potential in image restoration.