Blind image restoration is a non-convex problem which involves restoration of images from an unknown blur kernel. The factors affecting the performance of this restoration are how much prior information about an image and a blur kernel are provided and what algorithm is used to perform the restoration task. Prior information on images is often employed to restore the sharpness of the edges of an image. By contrast, no consensus is still present regarding what prior information to use in restoring from a blur kernel due to complex image blurring processes. In this paper, we propose modelling of a blur kernel as a sparse linear combinations of basic 2-D patterns. Our approach has a competitive edge over the existing blur kernel modelling methods because our method has the flexibility to customize the dictionary design, which makes it well-adaptive to a variety of applications. As a demonstration, we construct a dictionary formed by basic patterns derived from the Kronecker product of Gaussian sequences. We also compare our results with those derived by other state-of-the-art methods, in terms of peak signal to noise ratio (PSNR).
The spatially variant cases are solved by dividing an image into blocks (of size depending on the supports of blur kernels) and then processing each block independently by a spatially invariant method. Computational complexity is one of the main concerns for the spatially variant methods, because fast Fourier transformation (FFT) can be applied only to spatially invariant cases but not to spatially variant ones. Some fast algorithms based on variable splitting techniques and proximal point methods have also been proposed @cite_24 @cite_20 . For example, the variable splitting technique is used in @cite_24 for the TV approach and in @cite_8 for statistical modelling of image gradients. Another topic of concern is the removal of boundary effects incurred from dividing an image into blocks @cite_28 such as the matting approach adopted in @cite_40 .
@cite_8 @cite_28 @cite_24 @cite_40 @cite_20
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The heavy-tailed distribution of gradients in natural scenes have proven effective priors for a range of problems such as denoising, deblurring and super-resolution. These distributions are well modeled by a hyper-Laplacian (p(x) ∝ e-k|x|α ), typically with 0.5 ≤ α ≤ 0.8. However, the use of sparse distributions makes the problem non-convex and impractically slow to solve for multi-megapixel images. In this paper we describe a deconvolution approach that is several orders of magnitude faster than existing techniques that use hyper-Laplacian priors. We adopt an alternating minimization scheme where one of the two phases is a non-convex problem that is separable over pixels. This per-pixel sub-problem may be solved with a lookup table (LUT). Alternatively, for two specific values of α, 1 2 and 2 3 an analytic solution can be found, by finding the roots of a cubic and quartic polynomial, respectively. Our approach (using either LUTs or analytic formulae) is able to deconvolve a 1 megapixel image in less than 3 seconds, achieving comparable quality to existing methods such as iteratively reweighted least squares (IRLS) that take 20 minutes. Furthermore, our method is quite general and can easily be extended to related image processing problems, beyond the deconvolution application demonstrated. Most existing nonblind image deblurring methods assume that the blur kernel is free of error. However, it is often unavoidable in practice that the input blur kernel is erroneous to some extent. Sometimes, the error could be severe, e.g., for images degraded by nonuniform motion blurring. When an inaccurate blur kernel is used as the input, significant distortions will appear in the image recovered by existing methods. In this paper, we present a novel convex minimization model that explicitly takes account of error in the blur kernel. The resulting minimization problem can be efficiently solved by the so-called accelerated proximal gradient method. In addition, a new boundary extension scheme is incorporated in the proposed model to further improve the results. The experiments on both synthesized and real images showed the efficiency and robustness of our algorithm to both the image noise and the model error in the blur kernel. We propose, analyze, and test an alternating minimization algorithm for recovering images from blurry and noisy observations with total variation (TV) regularization. This algorithm arises from a new half-quadratic model applicable to not only the anisotropic but also the isotropic forms of TV discretizations. The per-iteration computational complexity of the algorithm is three fast Fourier transforms. We establish strong convergence properties for the algorithm including finite convergence for some variables and relatively fast exponential (or @math -linear in optimization terminology) convergence for the others. Furthermore, we propose a continuation scheme to accelerate the practical convergence of the algorithm. Extensive numerical results show that our algorithm performs favorably in comparison to several state-of-the-art algorithms. In particular, it runs orders of magnitude faster than the lagged diffusivity algorithm for TV-based deblurring. Some extensions of our algorithm are also discussed. This paper addresses the problem of two-layer out-of-focus blur removal from a single image, in which either the foreground or the background is in focus while the other is out of focus. To recover details from the blurry parts, the existing blind deconvolution algorithms are insufficient as the problem is spatially variant. The proposed method exploits the invariant structure of the problem by first predicting the occluded background. Then a blind deconvolution algorithm is applied to estimate the blur kernel and a coarse estimate of the image is found as a side product. Finally, the blurred region is recovered using total variation minimization, and fused with the sharp region to produce the final deblurred image. Digital images often suffer from point spreading or blurring from both known and unknown filters or point spread functions. The sources of degradation can be lens point spreading, misfocus, motion, and scattering in case of x-ray images or atmospheric turbulence. Therefore a digital image can suffer blurring from a single or an combination of various point spread functions, for example many images suffer from lens out of focus blur because of manufacturing limitations or satellite aerial images suffer from lens focus and atmospheric turbulence etc. The obvious requirement of an imaging system is to reproduce an image that is as close to original as possible. Most existing image restoration methods uses blind deconvolution and deblurring methods that require good knowledge about both the signal and the filter and the performance depends on the amount of prior information regarding the blurring function and the signal. Often an iterative procedure is required for estimating the blurring function such as Richardson-Lucy method and is computational complex and expensive and sometime instable. This paper presents a blind image restoration method based on techniques of blind signal separation (BSS) in combination with the genetic algorithm for parameters optimization. The method is not only simple but also requires little priori knowledge regarding the signal and the blurring function.