Abstract: Most of blind deblurring methods are sensitive to image noise. Even a small amount of noise can degrade the quality of restoration image dramatically. Considering that blurry image contains both blur kernel information and clear image information implicitly, we employ a prior of convolutional kernel spectral, in combination with a hyper Laplacian prior of clear image in gradient domain, to establish optimization model for blind noisy image deblurring. This model is more reasonable than other models which do not make full use of the blurry image information, so our model can obtain more accurate estimation image. In this paper, the Hessian matrix is employed to generate a prior term by using the blurry image and a blur kernel together instead of just the clear image. The proposed model can be solved by an iterative scheme which alternatively refines the blur kernel and the estimation image. At the latent image restoration stage, the variable splitting method is adopted to calculate the clear image because of the hyper Laplacian prior term. Furthermore, clear images are obtained by using fast Fourier transformation and closed-form threshold formulas to speed up the optimization process. Experimental results show that, compared with other methods, the proposed method can obtain more robust blur kernel and more accurate clear image, and the convergence speed is faster.

Key words: blind deblurring, hyper Laplacian prior, convolution kernel spectra properties, general soft threshold, closed-form threshold