Abstract
Image restoration is one of the most fundamental issues in imaging science. Total variation regularization is widely used in image restoration problems for its capability to preserve edges. In this paper, we consider a constrained minimization problem with double total variation regularization terms. To solve this problem, we employ the split Bregman iteration method and the Chambolle’s algorithm. The convergence property of the algorithm is established. The numerical results demonstrate the effectiveness of the proposed method in terms of peak signal-to-noise ratio (PSNR) and the structure similarity index (SSIM).
Highlights
Image restoration is a fundamental problem in the literature of image processing
For FastTV, based on the suggestions in [2], we fixed its parameters α1 = 0.003 for blur signal-to-noise ratio (BSNR) = 40 dB and α1 = 0.006 for BSNR = 30 dB, and we determine the best value of α2 such as the restored images with best performance
This example consists in restoring the image “Lena” degraded by an out-of-focus blur with radius 3 and contaminated by BSNR = 30 white Gaussian noise
Summary
Image restoration is a fundamental problem in the literature of image processing. It plays an important role in various areas such as remote sensing, astronomy, medical imaging, and microscopy [1, 2]. In the original TV regularization paper [11], the authors proposed a time marching scheme to solve the associated Euler-Lagrange equation of (3). The drawback of this method is very slow due to stability constraints. Chambolle [15] considered a dual formulation of the TV denoising problem and proposed a semiimplicit gradient descent algorithm to solve the resulting constrained optimization problem. This method is globally convergent with a suitable step size.
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