The Study On Blind Image Restoration Algorithms

As a major branch and research focus in the image processing feld, the study onimage restoration is always of practical signifcance and applied value. Blind imagerestoration has always been one of the most difcult problems in image restoration.In image restoration, the image degradation process is generally modeled as the linearspace constant system and the additive noise modelg(x, y)=h(x, y)*u(x, y)+n(x, y),where u(x, y), g(x, y) and n(x, y) denote the original image, the degraded image and theadditive white Gaussian noise with variance σ2, respectively. h(x, y) denotes the pointspread function (PSF).”” denotes the convolution operator. The degradation processis known to be an ill-posed problem. Most of the image restoration algorithms builton the known point spread function. But the point spread function is often unknownin practice. Therefore, the study on the image blind restoration is very necessary intheory and practice.For the blind restoration, we describe the details of the theory and the maincomputational methods in this paper. In view of the image motion blurring induced bythe relative motion between the camera and the subject, we presents the efective blindimage restoration method. The contributions of this paper are mainly as following:1. Present a blind image restoration algorithm based on the iteration method offrequency domain and the guided flter. Firstly, estimate the point spread function in frequency domain. The iteration formula in frequency domain is where F denotes the Fourier transfer operator, F(-)*denotes the complex conjugate of F, α1and α2are the constant. We estimate the approximate solution of the point spread function by the iteration algorithm in frequency domain.Secondly, the estimated approximation solution of the PSF is used as the initial value. The blind image restoration problem becomes to the non-blind image restoration problem. Because the guided filter has the edge-preserving smoothing property and could eliminate the noise and suppress the ringing, we restore the target image by the non-blind image restoration algorithm based on guided filter.We denote the guided filter as where uI and up denote the guidance image and the filtering input image, respectively. u denote the filtering output image. ω is the size of the choosing kernel, and ε>0is the regularization parameter.According to the two following functions where ue is the pre-estimated image, and λ>0is the regularization parameter. We take the solutions as the guidance image and the filtering input image, and then apply the guided filter to the image up in order to remove the noise. Thus we can obtain clearer image.By iterating the above two steps, we can obtain the original clear image.2. Present a blind image restoration algorithm based on the prediction of strong edges and the guided filter.Firstly, apply the strong edges information of the image to estimate the PSF. Because whether the smooth regions of the image are blurred or not does not much affect the quality. However, the strong edges after being blurred have great changes, so it is important to research how to use the strong edges of the blurred image to estimate the PSF. The strong edges (Px,Py) of the observed image u are calculated by where ux and uy denote the partial derivative of X and Y direction of the current estimated image, respectively. T is a threshold value. Then we use the following way to estimate the PSF: where (gx,gy) denotes the gradient of the image g. We use the steepest descent method to solve this extremum problem above in order to obtain the PSF.Secondly, with the estimated point spread function, we can obtain the restored image by the non-blind restoration algorithm based on guided filter. The proposed method could well preserve the edges of the image and suppress the ringing and noise. In order to verify the efectiveness of the proposed algorithm, we give severalgroups of experiments compared the proposed algorithms with others. The experi-mental results show that the proposed algorithm can not only efectively eliminate thenoise and suppress the ringing, but also well preserve the edge and texture details.Therefore, the proposed algorithm can restore a higher quality image.