Models based on total variation (TV) regularization are proven to be effective in removing random noise. However, the serious staircase effect also exists in the denoised images. In this study, two-dimensional total variation with overlapping group sparsity (OGS-TV) is applied to images with impulse noise, to suppress the staircase effect of the TV model and enhance the dissimilarity between smooth and edge regions. In the traditional TV model, the L1-norm is always used to describe the statistics characteristic of impulse noise. In this paper, the Lp-pseudo-norm regularization term is employed here to replace the L1-norm. The new model introduces another degree of freedom, which better describes the sparsity of the image and improves the denoising result. Under the accelerated alternating direction method of multipliers (ADMM) framework, Fourier transform technology is introduced to transform the matrix operation from the spatial domain to the frequency domain, which improves the efficiency of the algorithm. Our model concerns the sparsity of the difference domain in the image: the neighborhood difference of each point is fully utilized to augment the difference between the smooth and edge regions. Experimental results show that the peak signal-to-noise ratio, the structural similarity, the visual effect, and the computational efficiency of this new model are improved compared with state-of-the-art denoising methods.
Impulse Noise Denoising Using Total Variation with Overlapping Group Sparsity and Lp-Pseudo-Norm Shrinkage
