Image Denoising Using Lower Semi-Frames

A blind image denoising framework based on an infinite directional lower semi-frame (DLSF) is proposed for additive white Gaussian noise. The model employs scale-dependent directional analysis with resolvent regularization of the unbounded semi-frame operator. Noise variance is estimated directly in the DLSF domain by modeling the joint covariance of four directional difference channels and applying covariance whitening to obtain a chi-square statistic. A lower-tail moment estimator provides blind noise estimation without median absolute deviation. The estimated noise level is incorporated into channel-wise Wiener-type shrinkage and canonical-dual synthesis, followed by a data-consistent iterative reconstruction with automatic stopping. Experiments on three standard grayscale images at noise levels 15--30 yield a mean relative noise-estimation error of 3.28%, with average improvements of 7.45 dB in PSNR and 0.367 in SSIM. At 30/255 noise, the estimation error decreases to 1.73%, with a mean PSNR gain of 8.31 dB. Results demonstrate effective noise suppression and structural preservation, with the strongest performance on smooth and edge-dominated images.