Towards Image Denoising via Random Interpolation and Hard Thresholding

Image denoising refers to producing a crystal clear digital image from a noisy capture environment since the natural image is inevitably contaminated during phases of acquisition and transmission by different kinds of noises, such as salt and pepper noise (SAPN) and additive white Gaussian noise (AWGN). Towards the mixed noise removal, it is well known that the least squares-based metric is highly sensitive to outliers, and one common practice is using ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf>-norm minimization to restore the noise-free image. However, the resulting minimization problem is challenging to guarantee its convergence because of the nonconvexity of ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf>-norm. Moreover, its performance is greatly affected by the choice of p. On the basis of that, we propose to employ low-rank matrix factorization to form the basic denoising framework due to the advantage of preserving the spatial integrity of the image. Herein, the noisy image is randomly sampled to produce sampled image sets to mitigate the SPAN. An alternating minimization method is applied to all sampled images and the resultant images are fused via a wavelet fusion with hard threshold denoising. Since the sampled image sets have independent but identical noise property, the wavelet fusion serves as the effective means to remove the AWGN. Simulation results are presented vividly to show the impressive performance in both subjective and objective metrics.