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65
Nonuniform deblurring for shaken images
 In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2010. 8. Image taken with a Canon 1D Mark III, at 35mm f/4.5. Images
"... Blur from camera shake is mostly due to the 3D rotation of the camera, resulting in a blur kernel that can be significantly nonuniform 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 p ..."
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Cited by 75 (4 self)
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Blur from camera shake is mostly due to the 3D rotation of the camera, resulting in a blur kernel that can be significantly nonuniform 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. 1.
Image deblurring and superresolution by adaptive sparse domain selection and adaptive regularization
 IEEE Trans. Image Process
, 2011
"... Abstract—As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of thenorm optimization techniques and the fact that natural images are intrinsically ..."
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Cited by 59 (11 self)
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Abstract—As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of thenorm optimization techniques and the fact that natural images are intrinsically sparse in some domains. The image restoration quality largely depends on whether the employed sparse domain can represent well the underlying image. Considering that the contents can vary significantly across different images or different patches in a single image, we propose to learn various sets of bases from a precollected dataset of example image patches, and then, for a given patch to be processed, one set of bases are adaptively selected to characterize the local sparse domain. We further introduce two adaptive regularization terms into the sparse representation framework. First, a set of autoregressive (AR) models are learned from the dataset of example image patches. The best fitted AR models to a given patch are adaptively selected to regularize the image local structures. Second, the image nonlocal selfsimilarity is introduced as another regularization term. In addition, the sparsity regularization parameter is adaptively estimated for better image restoration performance. Extensive experiments on image deblurring and superresolution validate that by using adaptive sparse domain selection and adaptive regularization, the proposed method achieves much better results than many stateoftheart algorithms in terms of both PSNR and visual perception. Index Terms—Deblurring, image restoration (IR), regularization, sparse representation, superresolution. I.
Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
, 2010
"... A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAPEM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is describe ..."
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Cited by 55 (8 self)
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A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAPEM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAPEM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost. 1 I.
Flexible Depth of Field Photography ⋆
"... Abstract. The range of scene depths that appear focused in an image is known as the depth of field (DOF). Conventional cameras are limited by a fundamental tradeoff between depth of field and signaltonoise ratio (SNR). For a dark scene, the aperture of the lens must be opened up to maintain SNR, ..."
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Cited by 42 (8 self)
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Abstract. The range of scene depths that appear focused in an image is known as the depth of field (DOF). Conventional cameras are limited by a fundamental tradeoff between depth of field and signaltonoise ratio (SNR). For a dark scene, the aperture of the lens must be opened up to maintain SNR, which causes the DOF to reduce. Also, today’s cameras have DOFs that correspond to a single slab that is perpendicular to the optical axis. In this paper, we present an imaging system that enables one to control the DOF in new and powerful ways. Our approach is to vary the position and/or orientation of the image detector, during the integration time of a single photograph. Even when the detector motion is very small (tens of microns), a large range of scene depths (several meters) is captured both in and out of focus. Our prototype camera uses a microactuator to translate the detector along the optical axis during image integration. Using this device, we demonstrate three applications of flexible DOF. First, we describe extended
Nonlocally Centralized Sparse Representation for Image Restoration
, 2011
"... The sparse representation models code an image patch as a linear combination of a few atoms chosen out from an overcomplete dictionary, and they have shown promising results in various image restoration applications. However, due to the degradation of the observed image (e.g., noisy, blurred and/o ..."
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Cited by 25 (8 self)
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The sparse representation models code an image patch as a linear combination of a few atoms chosen out from an overcomplete dictionary, and they have shown promising results in various image restoration applications. However, due to the degradation of the observed image (e.g., noisy, blurred and/or downsampled), the sparse representations by conventional models may not be accurate enough for a faithful reconstruction of the original image. To improve the performance of sparse representation based image restoration, in this paper the concept of sparse coding noise is introduced, and the goal of image restoration turns to how to suppress the sparse coding noise. To this end, we exploit the image nonlocal selfsimilarity to obtain good estimates of the sparse coding coefficients of the original image, and then centralize the sparse coding coefficients of the observed image to those estimates. The socalled nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model, while our extensive experiments on various types of image restoration problems, including denoising, deblurring and superresolution, validate the generality and stateoftheart performance of the proposed NCSR algorithm.
A SURE Approach for Digital Signal/Image Deconvolution Problems
, 2009
"... In this paper, we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white Gaussian noise. The originality of the proposed approach is twofold. Firstly, we formulate the restoration problem as a nonlinear estimation problem leading to the mini ..."
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Cited by 22 (3 self)
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In this paper, we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white Gaussian noise. The originality of the proposed approach is twofold. Firstly, we formulate the restoration problem as a nonlinear estimation problem leading to the minimization of a criterion derived from Stein’s unbiased quadratic risk estimate. Secondly, the deconvolution procedure is performed using any analysis and synthesis frames that can be overcomplete or not. New theoretical results concerning the calculation of the variance of the Stein’s risk estimate are also provided in this work. Simulations carried out on natural images show the good performance of our method w.r.t. conventional waveletbased restoration methods.
Diffusion coded photography for extended depth of field
 in Proc. SIGGRAPH, 2010
"... Figure 1: Extending depth of field with diffusion coding for a scene consisting of three stuffed animals placed at different depths. (a) An image captured with a 50mm F/1.8 Canon Lens. The foreground and background objects exhibit severe defocus blur. (d) The diffusion coded image after deblurring. ..."
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Cited by 20 (7 self)
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Figure 1: Extending depth of field with diffusion coding for a scene consisting of three stuffed animals placed at different depths. (a) An image captured with a 50mm F/1.8 Canon Lens. The foreground and background objects exhibit severe defocus blur. (d) The diffusion coded image after deblurring. The image was captured with the diffuser from Section 6 placed in the lens aperture. (bc) Magnified regions from (a) and (d) that show that diffusion coding preserves details in foreground and background objects. In recent years, several cameras have been introduced which extend depth of field (DOF) by producing a depthinvariant point spread function (PSF). These cameras extend DOF by deblurring a captured image with a single spatiallyinvariant PSF. For these cameras, the quality of recovered images depends both on the magnitude of the PSF spectrum (MTF) of the camera, and the similarity between PSFs at different depths. While researchers have compared the MTFs of different extended DOF cameras, relatively little attention has been paid to evaluating their depth invariances. In this paper, we compare the depth invariance of several cameras, and introduce a new diffusion coding camera that achieves near identical performance to a focal sweep camera, but without the need for moving parts. Our technique utilizes a novel optical element placed in the pupil plane of an imaging system. Whereas previous approaches use optical elements characterized by their amplitude or phase profile, our approach utilizes one whose behavior is characterized by its scattering properties. Such an element is commonly referred to as an optical diffuser, and thus we refer to our new approach as diffusion coding. We show that diffusion coding can be analyzed in a simple and intuitive way by modeling the effect of a diffuser as a kernel in light field space. We provide detailed analysis of diffusion coded cameras and show results from an implementation using a custom designed diffuser.
Centralized sparse representation for image restoration
 in Proc. IEEE Int. Conf. on Computer Vision (ICCV
, 2011
"... This paper proposes a novel sparse representation model called centralized sparse representation (CSR) for image restoration tasks. In order for faithful image reconstruction, it is expected that the sparse coding coefficients of the degraded image should be as close as possible to those of the unkn ..."
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Cited by 18 (8 self)
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This paper proposes a novel sparse representation model called centralized sparse representation (CSR) for image restoration tasks. In order for faithful image reconstruction, it is expected that the sparse coding coefficients of the degraded image should be as close as possible to those of the unknown original image with the given dictionary. However, since the available data are the degraded (noisy, blurred and/or downsampled) versions of the original image, the sparse coding coefficients are often not accurate enough if only the local sparsity of the image is considered, as in many existing sparse representation models. To make the sparse coding more accurate, a centralized sparsity constraint is introduced by exploiting the nonlocal image statistics. The local sparsity and the nonlocal sparsity constraints are unified into a variational framework for optimization. Extensive experiments on image restoration validated that our CSR model achieves convincing improvement over previous stateoftheart methods. 1.
1 A Nonlocal TransformDomain Filter for Volumetric Data Denoising
"... Abstract—We present an extension of the BM3D filter to volumetric data. The proposed algorithm, denominated BM4D, implements the grouping and collaborative filtering paradigm, where mutually similar ddimensional patches are stacked together in a (d + 1)dimensional array and jointly filtered in tra ..."
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Cited by 12 (3 self)
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Abstract—We present an extension of the BM3D filter to volumetric data. The proposed algorithm, denominated BM4D, implements the grouping and collaborative filtering paradigm, where mutually similar ddimensional patches are stacked together in a (d + 1)dimensional array and jointly filtered in transform domain. While in BM3D the basic data patches are blocks of pixels, in BM4D we utilize cubes of voxels, which are stacked into a fourdimensional “group”. The fourdimensional transform applied on the group simultaneously exploits the local correlation present among voxels in each cube and the nonlocal correlation between the corresponding voxels of different cubes. Thus, the spectrum of the group is highly sparse, leading to very effective separation of signal and noise through coefficients shrinkage. After inverse transformation, we obtain estimates of each grouped cube, which are then adaptively aggregated at their original locations. We evaluate the algorithm on denoising of volumetric data corrupted by Gaussian and Rician noise, as well as on reconstruction of phantom data from sparse Fourier measurements. Experimental results demonstrate the stateoftheart denoising performance of BM4D, and its effectiveness when exploited as a regularizer in volumetric data reconstruction. Index Terms—Volumetric data denoising, volumetric data reconstruction, compressed sensing, magnetic resonance imaging, computed tomography, nonlocal methods, adaptive transforms I.
Hessian SchattenNorm Regularization for Linear Inverse Problems
, 2013
"... We introduce a novel family of invariant, convex, and nonquadratic functionals that we employ to derive regularized solutions of illposed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which are computed at every pixel of the image. Th ..."
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Cited by 11 (8 self)
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We introduce a novel family of invariant, convex, and nonquadratic functionals that we employ to derive regularized solutions of illposed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which are computed at every pixel of the image. They can be viewed as secondorder extensions of the popular totalvariation (TV) seminorm since they satisfy the same invariance properties. Meanwhile, by taking advantage of secondorder derivatives, they avoid the staircase effect, a common artifact of TVbased reconstructions, and perform well for a wide range of applications. To solve the corresponding optimization problems, we propose an algorithm that is based on a primaldual formulation. A fundamental ingredient of this algorithm is the projection of matrices onto Schatten norm balls of arbitrary radius. This operation is performed efficiently based on a direct link we provide between vector projections onto ℓq norm balls and matrix projections onto Schatten norm balls. Finally, we demonstrate the effectiveness of the proposed methods through experimental results on several inverse imaging problems with real and simulated data.