Regularized Image Restoration Algorithm Based on the L-Curve Criterion

For the restoration of blurred image caused by atmospheric turbulence, the regularization function was added to discrepancy function to ensure that the linear system to be solved is well-posed. The parametric curve for restoring blurred image can be obtained, which coordinates are discrepancy function and regularization function, respectively. The left end portion of the curve was fitted with cubic polynomial, and the parameter corresponding to the maximum curvature point in L-curve was selected as optimal regularization parameter. When image boundary satisfy periodic condition, the block circulant matrix could be diagonalized by Fourier matrix, and then the restored image was received by solving linear systems with two-dimensional discrete Fourier transform and its inverse transform. Experimental results show that when the noise variance is small, the satisfactory recovery results could be achieved.