Fractional Fourier-Contourlet Deblurring of Space Variant Degradation Coupled with Noise

Fourier domain deblurring methods are not fit for space variant degradation due to time invariant property of the Fourier transform (FT). Filtering in the fractional Fourier transform (FRFT) domain can deblur space variant degradation effectively, but hardly denoise substantially in the meantime. We propose a fractional Fourier-contourlet restoration algorithm to remove the space variant blur and the white Gaussian noise in images. The deblurring is realized by the fractional Fourier filtering while denoising through the coutourlet shrinkage. Our hybrid scheme is based on the MSE minimization principle. This scheme resolves the problem of contradiction between deblurring and denoising in a single transform domain. Experiments demonstrate that the proposed algorithm can yield favorable performance to satisfy both sides of deblurring and denoising.