A new Tikhonov regularization method of Fuhry and Reichel [A new
Tikhonov regularization method, Numerical Algorithms, 59:433-445, 2011]
exhibits the excellent properties for ill-posed problems, but it can only deal
with small or moderate size problems because of the expensive computation
of singular value decomposition (SVD). In this paper, we extend the above
new Tikhonov regularization method to solve large-scale problems, e.g.,
image restoration problem with periodic boundary conditions, and realize
this extending by applying Fast Fourier Transformation (FFT) algorithm
to the spectral decomposition of the block circulant with circulant blocks
(BCCB) matrices. Experimental results confirm the superiority of our new
method.