Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> Photographs acquired under low-light conditions require long exposure times and therefore exhibit significant blurring due to the shaking of the camera. Using shorter exposure times results in sharper images but with a very high level of noise. In this paper we address this problem and present a novel blind deconvolution algorithm for a pair of differently exposed images. We formulate the problem in a hierarchical Bayesian framework by utilizing prior knowledge on the unknown image and blur, and also on the dependency between two observed images. By incorporating a fully Bayesian analysis, the developed algorithm estimates all necessary algorithm parameters along with the unknowns, such that no user-intervention is needed. Moreover, we employ a variational Bayesian inference procedure, which allows for the statistical compensation of errors occurring at different stages of the restoration, and also provides uncertainties of the estimates. Experimental results demonstrate the high restoration performance of the proposed algorithm. <s> BIB001 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> Modelling camera shake as a space-invariant convolution simplifies the problem of removing camera shake, but often insufficiently models actual motion blur such as those due to camera rotation and movements outside the sensor plane or when objects in the scene have different distances to the camera. In an effort to address these limitations, (i) we introduce a taxonomy of camera shakes, (ii) we build on a recently introduced framework for space-variant filtering by Hirsch et al. and a fast algorithm for single image blind deconvolution for space-invariant filters by Cho and Lee to construct a method for blind deconvolution in the case of space-variant blur, and (iii), we present an experimental setup for evaluation that allows us to take images with real camera shake while at the same time recording the space-variant point spread function corresponding to that blur. Finally, we demonstrate that our method is able to deblur images degraded by spatially-varying blur originating from real camera shake, even without using additionally motion sensor information. <s> BIB002 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> We present a deblurring algorithm that uses a hardware attachment coupled with a natural image prior to deblur images from consumer cameras. Our approach uses a combination of inexpensive gyroscopes and accelerometers in an energy optimization framework to estimate a blur function from the camera's acceleration and angular velocity during an exposure. We solve for the camera motion at a high sampling rate during an exposure and infer the latent image using a joint optimization. Our method is completely automatic, handles per-pixel, spatially-varying blur, and out-performs the current leading image-based methods. Our experiments show that it handles large kernels -- up to at least 100 pixels, with a typical size of 30 pixels. We also present a method to perform "ground-truth" measurements of camera motion blur. We use this method to validate our hardware and deconvolution approach. To the best of our knowledge, this is the first work that uses 6 DOF inertial sensors for dense, per-pixel spatially-varying image deblurring and the first work to gather dense ground-truth measurements for camera-shake blur. <s> BIB003 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> We describe a novel approach to reduce spatially varying motion blur in video and images using a hybrid camera system. A hybrid camera is a standard video camera that is coupled with an auxiliary low-resolution camera sharing the same optical path but capturing at a significantly higher frame rate. The auxiliary video is temporally sharper but at a lower resolution, while the lower frame-rate video has higher spatial resolution but is susceptible to motion blur. Our deblurring approach uses the data from these two video streams to reduce spatially varying motion blur in the high-resolution camera with a technique that combines both deconvolution and super-resolution. Our algorithm also incorporates a refinement of the spatially varying blur kernels to further improve results. Our approach can reduce motion blur from the high-resolution video as well as estimate new high-resolution frames at a higher frame rate. Experimental results on a variety of inputs demonstrate notable improvement over current state-of-the-art methods in image/video deblurring. <s> BIB004 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> Blur from camera shake is mostly due to the 3D rotation of the camera, resulting in a blur kernel that can be significantly non-uniform across the image. However, most current deblurring methods model the observed image as a convolution of a sharp image with a uniform blur kernel. We propose a new parametrized geometric model of the blurring process in terms of the rotational velocity of the camera during exposure. We apply this model to two different algorithms for camera shake removal: the first one uses a single blurry image (blind deblurring), while the second one uses both a blurry image and a sharp but noisy image of the same scene. We show that our approach makes it possible to model and remove a wider class of blurs than previous approaches, including uniform blur as a special case, and demonstrate its effectiveness with experiments on real images. <s> BIB005 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> Photo deblurring has been a major research topic in the past few years. So far, existing methods have focused on removing the blur due to camera shake and object motion. In this paper, we show that the optical system of the camera also generates significant blur, even with professional lenses. We introduce a method to estimate the blur kernel densely over the image and across multiple aperture and zoom settings. Our measures show that the blur kernel can have a non-negligible spread, even with top-of-the-line equipment, and that it varies nontrivially over this domain. In particular, the spatial variations are not radially symmetric and not even left-right symmetric. We develop and compare two models of the optical blur, each of them having its own advantages. We show that our models predict accurate blur kernels that can be used to restore photos. We demonstrate that we can produce images that are more uniformly sharp unlike those produced with spatially-invariant deblurring techniques. <s> BIB006 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> Camera shake leads to non-uniform image blurs. State-of-the-art methods for removing camera shake model the blur as a linear combination of homographically transformed versions of the true image. While this is conceptually interesting, the resulting algorithms are computationally demanding. In this paper we develop a forward model based on the efficient filter flow framework, incorporating the particularities of camera shake, and show how an efficient algorithm for blur removal can be obtained. Comprehensive comparisons on a number of real-world blurry images show that our approach is not only substantially faster, but it also leads to better deblurring results. <s> BIB007 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> This paper addresses how to model and correct image blur that arises when a camera undergoes ego motion while observing a distant scene. In particular, we discuss how the blurred image can be modeled as an integration of the clear scene under a sequence of planar projective transformations (i.e., homographies) that describe the camera's path. This projective motion path blur model is more effective at modeling the spatially varying motion blur exhibited by ego motion than conventional methods based on space-invariant blur kernels. To correct the blurred image, we describe how to modify the Richardson-Lucy (RL) algorithm to incorporate this new blur model. In addition, we show that our projective motion RL algorithm can incorporate state-of-the-art regularization priors to improve the deblurred results. The projective motion path blur model, along with the modified RL algorithm, is detailed, together with experimental results demonstrating its overall effectiveness. Statistical analysis on the algorithm's convergence properties and robustness to noise is also provided. <s> BIB008 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> Photographs taken in low-light conditions are often blurry as a result of camera shake, i.e. a motion of the camera while its shutter is open. Most existing deblurring methods model the observed blurry image as the convolution of a sharp image with a uniform blur kernel. However, we show that blur from camera shake is in general mostly due to the 3D rotation of the camera, resulting in a blur that can be significantly non-uniform across the image. We propose a new parametrized geometric model of the blurring process in terms of the rotational motion of the camera during exposure. This model is able to capture non-uniform blur in an image due to camera shake using a single global descriptor, and can be substituted into existing deblurring algorithms with only small modifications. To demonstrate its effectiveness, we apply this model to two deblurring problems; first, the case where a single blurry image is available, for which we examine both an approximate marginalization approach and a maximum a posteriori approach, and second, the case where a sharp but noisy image of the scene is available in addition to the blurry image. We show that our approach makes it possible to model and remove a wider class of blurs than previous approaches, including uniform blur as a special case, and demonstrate its effectiveness with experiments on synthetic and real images. <s> BIB009 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> Non-blind deconvolution is a key component in image deblurring systems. Previous deconvolution methods assume a linear blur model where the blurred image is generated by a linear convolution of the latent image and the blur kernel. This assumption often does not hold in practice due to various types of outliers in the imaging process. Without proper outlier handling, previous methods may generate results with severe ringing artifacts even when the kernel is estimated accurately. In this paper we analyze a few common types of outliers that cause previous methods to fail, such as pixel saturation and non-Gaussian noise. We propose a novel blur model that explicitly takes these outliers into account, and build a robust non-blind deconvolution method upon it, which can effectively reduce the visual artifacts caused by outliers. The effectiveness of our method is demonstrated by experimental results on both synthetic and real-world examples. <s> BIB010 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> 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. <s> BIB011 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> Blind deconvolution, which comprises simultaneous blur and image estimations, is a strongly ill-posed problem. It is by now well known that if multiple images of the same scene are acquired, this multichannel (MC) blind deconvolution problem is better posed and allows blur estimation directly from the degraded images. We improve the MC idea by adding robustness to noise and stability in the case of large blurs or if the blur size is vastly overestimated. We formulate blind deconvolution as an l(1) -regularized optimization problem and seek a solution by alternately optimizing with respect to the image and with respect to blurs. Each optimization step is converted to a constrained problem by variable splitting and then is addressed with an augmented Lagrangian method, which permits simple and fast implementation in the Fourier domain. The rapid convergence of the proposed method is illustrated on synthetically blurred data. Applicability is also demonstrated on the deconvolution of real photos taken by a digital camera. <s> BIB012 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> This paper addresses the problem of restoring images subjected to unknown and spatially varying blur caused by defocus or linear (say, horizontal) motion. The estimation of the global (non-uniform) image blur is cast as a multi-label energy minimization problem. The energy is the sum of unary terms corresponding to learned local blur estimators, and binary ones corresponding to blur smoothness. Its global minimum is found using Ishikawa's method by exploiting the natural order of discretized blur values for linear motions and defocus. Once the blur has been estimated, the image is restored using a robust (non-uniform) deblurring algorithm based on sparse regularization with global image statistics. The proposed algorithm outputs both a segmentation of the image into uniform-blur layers and an estimate of the corresponding sharp image. We present qualitative results on real images, and use synthetic data to quantitatively compare our approach to the publicly available implementation of Chakrabarti~et al. <s> BIB013 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> We address how to recover a blurred image with nonuniform blur kernel when the camera moves with a constant velocity in front of a static scene. We modeled the blur kernel as a series of parameterized projective transform matrices and the blurred image as an integration of the distorted clear image sequences. By formulating the problem as a convex optimization algorithm, this problem using gradient descent algorithm can be solved. In particular, we show how to incorporate the camera’s constant movements into the projection model. By doing so, the previous nonblind nonuniform projective motion path model is changed into a blind nonuniform model. The effectiveness of our method is demonstrated by conducting experimental comparisons with other popular image deblur algorithms. <s> BIB014 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> In light-limited situations, camera motion blur is one of the prime causes for poor image quality. Recovering the blur kernel and latent image from the blurred observation is an inherently ill-posed problem. In this paper, we introduce a hand-held multispectral camera to capture a pair of blurred image and Near-InfraRed (NIR) flash image simultaneously and analyze the correlation between the pair of images. To utilize the high-frequency details of the scene captured by the NIR-flash image, we exploit the NIR gradient constraint as a new type of image regularization, and integrate it into a Maximum-A-Posteriori (MAP) problem to iteratively perform the kernel estimation and image restoration. We demonstrate our method on the synthetic and real images with both spatially invariant and spatially varying blur. The experiments strongly support the effectiveness of our method to provide both accurate kernel estimation and superior latent image with more details and fewer ringing artifacts. <s> BIB015 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> In this paper we propose a space-variant blur estimation and effective denoising/deconvolution method for combining a long exposure blurry image with a short exposure noisy one. The blur in the long exposure shot is mainly caused by camera shake or object motion, and the noise in the underexposed image is introduced by the gain factor applied to the sensor when the ISO is set to an high value. Due to the space variant degradation, the image pair is divided into overlapping patches for processing. The main idea in the deconvolution algorithm is to incorporate a combination of prior image models into a spatially-varying deblurring/denoising framework which is applied to each patch. The method employs a kernel and parameter estimation method to choose between denoising or deblurring each patch. Experiments on both synthetic and real images are provided to validate the proposed approach. <s> BIB016 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> To correct geometric distortion and reduce space and time-varying blur, a new approach is proposed in this paper capable of restoring a single high-quality image from a given image sequence distorted by atmospheric turbulence. This approach reduces the space and time-varying deblurring problem to a shift invariant one. It first registers each frame to suppress geometric deformation through B-spline-based nonrigid registration. Next, a temporal regression process is carried out to produce an image from the registered frames, which can be viewed as being convolved with a space invariant near-diffraction-limited blur. Finally, a blind deconvolution algorithm is implemented to deblur the fused image, generating a final output. Experiments using real data illustrate that this approach can effectively alleviate blur and distortions, recover details of the scene, and significantly improve visual quality. <s> BIB017 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> Hand-held cameras inevitably result in blurred images caused by camera-shake, and even more so in high dynamic range imaging applications where multiple images are captured over a wide range of exposure settings. The degree of blurring depends on many factors such as exposure time, stability of the platform, and user experience. Camera shake involves not only translations but also rotations resulting in nonuniform blurring. In this paper, we develop a method that takes input non-uniformly blurred and differently exposed images to extract the deblurred, latent irradiance image. We use transformation spread function (TSF) to effectively model the blur caused by camera motion. We first estimate the TSFs of the blurred images from locally derived point spread functions by exploiting their linear relationship. The scene irradiance is then estimated by minimizing a suitably derived cost functional. Two important cases are investigated wherein 1) only the higher exposures are blurred and 2) all the captured frames are blurred. <s> BIB018 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> In this paper, we address the problem of estimating a latent sharp image from a single spatially variant blurred image. Non-uniform deblurring methods based on projective motion path models formulate the blur as a linear combination of homographic projections of a clear image. But they are computationally expensive and require large memory due to the calculation and storage of a large number of the projections. Patch-wise non-uniform deblurring algorithms have been proposed to estimate each kernel locally by a uniform deblurring algorithm, which does not require to calculate and store the projections. The key issues of these methods are the accuracy of kernel estimation and the identification of erroneous kernels. To perform accurate kernel estimation, we employ the total variation (TV) regularization to recover a latent image, in which the edges are better enhanced and the ringing artifacts are reduced, rather than Tikhonov regularization that previous algorithms adopt. Thus blur kernels can be estimated more accurately from the latent image and estimated in a closed form while previous methods cannot estimate kernels in closed forms. To identify the erroneous kernels, we develop a novel metric, which is able to measure the similarity between the neighboring kernels. After replacing the erroneous kernels with the well-estimated ones, a clear image is obtained. The experiments show that our approach can achieve better results on the real-world blurry images while using less computation and memory. <s> BIB019 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> Blur kernel estimation is a crucial step in the deblurring process for images. Estimation of the kernel, especially in the presence of noise, is easily perturbed, and the quality of the resulting deblurred images is hence degraded. Since every motion blur in a single exposure image can be represented by 2D parametric curves, we adopt a piecewise-linear model to approximate the curves for the reliable blur kernel estimation. The model is found to be an effective tradeoff between flexibility and robustness as it takes advantage of two extremes: (1) the generic model, represented by a discrete 2D function, which has a high degree of freedom (DOF) for the maximum flexibility but suffers from noise and (2) the linear model, which enhances robustness and simplicity but has limited expressiveness due to its low DOF. We evaluate several deblurring methods based on not only the generic model, but also the piecewise-linear model as an alternative. After analyzing the experiment results using real-world images with significant levels of noise and a benchmark data set, we conclude that the proposed model is not only robust with respect to noise, but also flexible in dealing with various types of blur. <s> BIB020 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> The capture of multiple images is a simple way to increase the chance of capturing a good photo with a light-weight hand-held camera, for which the camera-shake blur is typically a nuisance problem. The naive approach of selecting the single best captured photo as output does not take full advantage of all the observations. Conventional multi-image blind deblurring methods can take all observations as input but usually require the multiple images are well aligned. However, the multiple blurry images captured in the presence of camera shake are rarely free from mis-alignment. Registering multiple blurry images is a challenging task due to the presence of blur while deblurring of multiple blurry images requires accurate alignment, leading to an intrinsically coupled problem. In this paper, we propose a blind multi-image restoration method which can achieve joint alignment, non-uniform deblurring, together with resolution enhancement from multiple low-quality images. Experiments on several real-world images with comparison to some previous methods validate the effectiveness of the proposed method. <s> BIB021 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> Texts in natural scenes carry critical semantic clues for understanding images. When capturing natural scene images, especially by handheld cameras, a common artifact, i.e., blur, frequently happens. To improve the visual quality of such images, deblurring techniques are desired, which also play an important role in character recognition and image understanding. In this paper, we study the problem of recovering the clear scene text by exploiting the text field characteristics. A series of text-specific multiscale dictionaries (TMD) and a natural scene dictionary is learned for separately modeling the priors on the text and nontext fields. The TMD-based text field reconstruction helps to deal with the different scales of strings in a blurry image effectively. Furthermore, an adaptive version of nonuniform deblurring method is proposed to efficiently solve the real-world spatially varying problem. Dictionary learning allows more flexible modeling with respect to the text field property, and the combination with the nonuniform method is more appropriate in real situations where blur kernel sizes are depth dependent. Experimental results show that the proposed method achieves the deblurring results with better visual quality than the state-of-the-art methods. <s> BIB022 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> Abstract In recent years, a lot of motion deblurring methods have been proposed, most of which divide the motion blur problem into two parts: camera shake and object motion, and just deal with only one side of the problem. As a result, in this paper we focus on seeking a effective model to handle these two kinds of motion blur simultaneously. An optical flow based model is then proposed. In particular, the blurred image can be formulated as an integration of some clear intermediate images after optical based transformed. Meanwhile an effective algorithm based on this new model is introduced to deblur different types of blurry images. In this work, we not only use the optical flow to represent the blur process but also derive the optical flow estimation algorithm to help estimate the non-uniform PSF for each pixel. In addition, we show that by incorporating different kinds of constraints our method can get more robust and stable results. The experiments on both synthesized and real images show that our algorithm can effectively recover the latent images and get comparable results with some state of the art algorithms. <s> BIB023 </s> Variational Bayesian Blind Image Deconvolution: A review <s> D. Spatially varying blur and other modeling problems <s> This paper proposes a simple, accurate, and robust approach to single image blind super-resolution (SR). This task is formulated as a functional to be minimized with respect to both an intermediate super-resolved image and a non- parametric blur-kernel. The proposed method includes a convolution consistency constraint which uses a non-blind learning-based SR result to better guide the estimation process. Another key component is the bi-l 0-l 2-norm regularization placed on the super-resolved, sharp image and the blur-kernel, which is shown to be quite beneficial for accurate blur-kernel estimation. The numerical optimization is implemented by coupling the splitting augmented Lagrangian and the conjugate gradient. With the pre-estimated blur-kernel, the final SR image is reconstructed using a simple TV-based non-blind SR method. The new method is demonstrated to achieve better performance than Michaeli and Irani [2] in both terms of the kernel estimation accuracy and image SR quality. <s> BIB024
In this paper we have assumed that the blur is the same across the image. However, as shown in BIB006 , even the camera optical system generates a considerable amount of spatially varying (SV) blur. In general, spatially varying degradation can be modeled as where y(s) is the value of the observed image at position s, x(u) is the value of the unknown ideal image at position u, h(s, s − u) is the blur affecting the image, that depends on each image pixel position, and n(s) is the noise. When SV BID is addressed, some restrictions are applied to the way the blur varies in Eq. (31) in order to make the problem feasible. Such restrictions include the assumption that the blur is piecewise-invariant or piecewise smooth spatially varying, that is, the blur varies smoothly in the image, or that the blur is piecewise constant and location dependent, that is, different regions in the image have different blurs but the blur is spatially-invariant in each region. Another typical restriction is to assume that the type of the blur is known, for example, it is due to camera shake, or to consider images of a certain type, such as images with text BIB022 or star fields  . One approach to SV BID is to divide the image into non-overlapping patches where the blur is assumed to be stationary, apply a BID method on each patch independently, and merge the restored patches to obtain the final image. If the patches are not predefined, this approach casts the SV BID into a segmentation problem BIB013 in which the simpler case is to consider just two regions, a focused foreground and a out-of-focus background BIB011 . If the patches overlap and the blur varies smoothly on the image, the degradation model in Eq. (31) can be approximated as where w r (u) ≥ 0, r w r (u) = 1, are weights allowing the smooth blending of the overlapping patches BIB002 . The advantage of this model is that it allows for an efficiently implementation using the Efficient Flow Filter (EFF) method BIB007 and also for different types of blur. On the other hand, its accuracy depends on the accuracy of the estimated kernel and may produce large errors if the kernels are not precisely estimated. In BIB019 the EFF method is extended to handle TV priors and a method to detect and replace erroneous blurs is proposed making it more robust. Another method to estimate smoothly varying blurs, with applications to star field images, is propossed in  . The method estimates the blur at certain image positions and uses SVD to remove outliers and estimate a smooth PSF field from the individual PSFs. If only camera-shake blur is considered, the Projective Motion Path approach BIB008 models the SV degradation as the average of multiple sharp images, each one corresponding to one of all possible camera poses, that is, where H i are homographies, that is, combinations of rotations and translations, that project the sharp image given a camera orientation. The homographies can be obtained from auxiliary sensors attached to the camera, such as gyroscopes (see BIB003 and section IV-E), and high speed low resolution cameras BIB004 , or they are estimated with the image BIB014 . A similar approximation is considered in BIB005 where the SV degradation is modeled as a weighted sum of sharp images obtained at all possible camera poses, that is, where C i is the matrix that applies the homography H i to the image x and w(i) weights the i-th projection depending on the time spent by the camera at the i-th pose during the capture time. In BIB009 , VB is used to estimate both the image x and the weights w(·). The drawback of this approach is that is resource demanding since it has to compute and store all the projections. To alleviate this problem,  proposes an iterative method that, at each iteration, restricts the solution space to a small set of camera poses which the camera motion trajectory is most likely to belong to. Despite all these advances, more research is still needed to solve the general SV BID problem as described by Eq. BIB020 . Even without mentioning the spatially variant nature of the blur, the linear model in Eq. (1), utilized by most BID methods, is not a realistic one for real-life images. BIB010 . We believe that developing methods that explicitly handle such model violations will improve the applicability of BID to real problems. These modeling problems are alleviated with the use of more than one images. Considering color and, in general, multichannel images, remedies, to a great extend, the ill-posed nature of blind deconvolution BIB012 . Using image pairs with different properties facilitates blur estimation and helps handle saturated pixels and other camera imperfections. For instance, in BIB015 a near-infrared image is captured together with a visible blurred image and, in BIB001 , BIB016 a low exposure sharp but noisy image is used to improve the restoration results. If video is available, techniques can take into account the motion between frames [91]- BIB023 to tackle the deblurring problem. Of interest is also the approach in BIB017 where a single highquality image is obtained from a sequence of images distorted by atmospheric turbulence. Having several images also allows blind image deconvolution to be addressed simultaneously with other problems, such as, super-resolution (see, for instance, BIB024 or BIB021 ) or high dynamic rage (HDR) imaging BIB018 . Finally, to conclude this section on modeling, we would like to mention the need to model what a good restoration is. We believe that more BID software applications will be developed if the quality of a restored image can be assessed, without human intervention, before presenting it to the user.