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).
Among all different forms of regularizations on images, the total variation (TV) regularization function and its variations have been widely used @cite_16 @cite_17 @cite_21 @cite_39 @cite_11 @cite_34 @cite_31 @cite_27 @cite_6 @cite_35 @cite_26 @cite_30 @cite_32 . Statistical models on the gradients of natural images have been adopted for image prior @cite_36 @cite_45 . Sparse assumptions have been used to model representation coefficients for natural images in a transform domain @cite_38 @cite_20 or in an image domain @cite_4 . A counter-intuitive finding is reported in @cite_36 indicating that most cost functions for image prior prefer blurry images to sharp images, as blurry images have lower costs than sharp images. Attempt is made in @cite_1 to achieve the lowest cost for true sharp image by introducing an @math function on images.
@cite_30 @cite_35 @cite_36 @cite_20 @cite_38 @cite_4 @cite_21 @cite_39 @cite_17 @cite_26 @cite_32 @cite_6 @cite_27 @cite_34 @cite_16 @cite_1 @cite_45 @cite_31 @cite_11
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A conventional camera captures blurred versions of scene information away from the plane of focus. Camera systems have been proposed that allow for recording all-focus images, or for extracting depth, but to record both simultaneously has required more extensive hardware and reduced spatial resolution. We propose a simple modification to a conventional camera that allows for the simultaneous recovery of both (a) high resolution image information and (b) depth information adequate for semi-automatic extraction of a layered depth representation of the image. Our modification is to insert a patterned occluder within the aperture of the camera lens, creating a coded aperture. We introduce a criterion for depth discriminability which we use to design the preferred aperture pattern. Using a statistical model of images, we can recover both depth information and an all-focus image from single photographs taken with the modified camera. A layered depth map is then extracted, requiring user-drawn strokes to clarify layer assignments in some cases. The resulting sharp image and layered depth map can be combined for various photographic applications, including automatic scene segmentation, post-exposure refocusing, or re-rendering of the scene from an alternate viewpoint. 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. We address the problem of image deconvolution under I sub p norm (and other) penalties expressed in the wavelet domain. We propose an algorithm based on the bound optimization approach; this approach allows deriving EM-type algorithms without using the concept of missing hidden data. The algorithm has provable monotonicity both with orthogonal or redundant wavelet transforms. We also derive bounds on the l sub p norm penalties to obtain closed form update equations for any p spl isin [0, 2]. Experimental results show that the proposed method achieves state-of-the-art performance. We propose a sparse representation based blind image deblurring method. The proposed method exploits the sparsity property of natural images, by assuming that the patches from the natural images can be sparsely represented by an over-complete dictionary. By incorporating this prior into the deblurring process, we can effectively regularize the ill-posed inverse problem and alleviate the undesirable ring effect which is usually suffered by conventional deblurring methods. Experimental results compared with state-of-the-art blind deblurring method demonstrate the effectiveness of the proposed method. This paper presents a fast deblurring method that produces a deblurring result from a single image of moderate size in a few seconds. We accelerate both latent image estimation and kernel estimation in an iterative deblurring process by introducing a novel prediction step and working with image derivatives rather than pixel values. In the prediction step, we use simple image processing techniques to predict strong edges from an estimated latent image, which will be solely used for kernel estimation. With this approach, a computationally efficient Gaussian prior becomes sufficient for deconvolution to estimate the latent image, as small deconvolution artifacts can be suppressed in the prediction. For kernel estimation, we formulate the optimization function using image derivatives, and accelerate the numerical process by reducing the number of Fourier transforms needed for a conjugate gradient method. We also show that the formulation results in a smaller condition number of the numerical system than the use of pixel values, which gives faster convergence. Experimental results demonstrate that our method runs an order of magnitude faster than previous work, while the deblurring quality is comparable. GPU implementation facilitates further speed-up, making our method fast enough for practical use. Blind image deconvolution is an ill-posed problem that requires regularization to solve. However, many common forms of image prior used in this setting have a major drawback in that the minimum of the resulting cost function does not correspond to the true sharp solution. Accordingly, a range of additional methods are needed to yield good results (Bayesian methods, adaptive cost functions, alpha-matte extraction and edge localization). In this paper we introduce a new type of image regularization which gives lowest cost for the true sharp image. This allows a very simple cost formulation to be used for the blind deconvolution model, obviating the need for additional methods. Due to its simplicity the algorithm is fast and very robust. We demonstrate our method on real images with both spatially invariant and spatially varying blur. We present a new algorithm for removing motion blur from a single image. Our method computes a deblurred image using a unified probabilistic model of both blur kernel estimation and unblurred image restoration. We present an analysis of the causes of common artifacts found in current deblurring methods, and then introduce several novel terms within this probabilistic model that are inspired by our analysis. These terms include a model of the spatial randomness of noise in the blurred image, as well a new local smoothness prior that reduces ringing artifacts by constraining contrast in the unblurred image wherever the blurred image exhibits low contrast. Finally, we describe an effficient optimization scheme that alternates between blur kernel estimation and unblurred image restoration until convergence. As a result of these steps, we are able to produce high quality deblurred results in low computation time. We are even able to produce results of comparable quality to techniques that require additional input images beyond a single blurry photograph, and to methods that require additional hardware.