Abstract
In this paper, a new model combining four-directional total variation with overlapping group sparsity is proposed, which not only suppresses the staircase effects introduced by traditional total variation, but also fully utilizes the gradient neighborhood information on each pixel of the image. In order to decrease the computation time of image denoising, the alternating direction method of multipliers (ADMM) is adopted to divide the complex optimization problem into separate subproblems that are easy to solve. At the same time, two-dimensional Fast Fourier Transform (FFT) and majorization-minimization (MM) are used to solve the subproblems alternatively. Then, the proposed new model is compared with other state-of-the-art models. Experiments show that the new model is robust in denoising. The new model not only excavates the gradient information of the four directions on the image to remove the noise more effectively, but also better in preserving image features, further reducing staircase artifacts.
Highlights
Due to the imperfection of an imaging system, images tend to be corrupted by different levels of noise during the progress of image capture, transmission, and storage, which can reduce image quality and cause image degradation
Liu et al [18] considered the total variation with overlapping group sparsity (OGSTV) for image restoration under Gaussian noise
We propose a new hybrid model called four-directional total variation with overlapping group sparsity (OGSTV4) by taking advantage of TV4 and OGSTV denoising model
Summary
Due to the imperfection of an imaging system, images tend to be corrupted by different levels of noise during the progress of image capture, transmission, and storage, which can reduce image quality and cause image degradation. Liu et al [18] considered the total variation with overlapping group sparsity (OGSTV) for image restoration under Gaussian noise This method extends the gradient of pixel level to the overlapping group sparse gradient in order to promote the difference between the smooth region and edge region and better suppress staircase effects. We propose a new hybrid model called four-directional total variation with overlapping group sparsity (OGSTV4) by taking advantage of TV4 and OGSTV denoising model. To reduce noise more comprehensively, Sakurai et al proposed a four-directional total variation model [26], which takes the image gradients in diagonal and back-diagonal directions into account to fully utilize the neighbor gradient information of each pixel. Where Dd ∈ Rmn×mn and Dv ∈ Rmn×mn represent the difference matrices in the diagonal and back-diagonal direction, respectively
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