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In this paper, we first propose two TVL1 variational problems for restoring images degraded by blurring and impulse noise, and then we propose two fixed-point-like methods, using proximal operators, for solving the new proposed TVL1 problems. Numerical experiments for several test images blurred by Gaussian kernel and corrupted by salt-and-pepper impulse noise are provided to demonstrate the efficiency and reliability of the proposed fixed-point-like methods. Numerical results show that two fixed-point-like methods for solving the new TVL1 variational problems perform very well in both PSNR (Peak signal-to-noise ratio) values and CPU time as compared with the fixed-point-like methods for solving two existing TVL1 variational problems.

Image Restoration Using Fixed-Point-Like Methods for New TVL1 Variational Problems