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57
Image Deblurring with Blurred/Noisy Image Pairs
"... Taking satisfactory photos under dim lighting conditions using a handheld camera is challenging. If the camera is set to a long exposure time, the image is blurred due to camera shake. On the other hand, the image is dark and noisy if it is taken with a short exposure time but with a high camera g ..."
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Cited by 129 (4 self)
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Taking satisfactory photos under dim lighting conditions using a handheld camera is challenging. If the camera is set to a long exposure time, the image is blurred due to camera shake. On the other hand, the image is dark and noisy if it is taken with a short exposure time but with a high camera gain. By combining information extracted from both blurred and noisy images, however, we show in this paper how to produce a high quality image that cannot be obtained by simply denoising the noisy image, or deblurring the blurred image alone. Our approach is image deblurring with the help of the noisy image. First, both images are used to estimate an accurate blur kernel, which otherwise is difficult to obtain from a single blurred image. Second, and again using both images, a residual deconvolution is proposed to significantly reduce ringing artifacts inherent to image deconvolution. Third, the remaining ringing artifacts in smooth image regions are further suppressed by a gaincontrolled deconvolution process. We demonstrate the effectiveness of our approach using a number of indoor and outdoor images taken by offtheshelf handheld cameras in poor lighting environments.
Degraded Image Analysis: An Invariant Approach
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 1998
"... Analysis and interpretation of an image which was acquired by a nonideal imaging system is the key problem in many application areas. The observed image is usually corrupted by blurring, spatial degradations, and random noise. Classical methods like blind deconvolution try to estimate the blur param ..."
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Cited by 64 (13 self)
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Analysis and interpretation of an image which was acquired by a nonideal imaging system is the key problem in many application areas. The observed image is usually corrupted by blurring, spatial degradations, and random noise. Classical methods like blind deconvolution try to estimate the blur parameters and to restore the image. In this paper, we propose an alternative approach. We derive the features for image representation which are invariant with respect to blur regardless of the degradation PSF provided that it is centrally symmetric. As we prove in the paper, there exist two classes of such features: the first one in the spatial domain and the second one in the frequency domain. We also derive socalled combined invariants, which are invariant to composite geometric and blur degradations. Knowing these features, we can recognize objects in the degraded scene without any restoration. Index TermsDegraded image, symmetric blur, blur invariants, image moments, combined invariant...
A novel blind deconvolution scheme for image restoration using recursive filtering
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 1998
"... In this paper, we present a novel blind deconvolution technique for the restoration of linearly degraded images without explicit knowledge of either the original image or the point spread function. The technique applies to situations in which the scene consists of a finite support object against a ..."
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Cited by 56 (5 self)
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In this paper, we present a novel blind deconvolution technique for the restoration of linearly degraded images without explicit knowledge of either the original image or the point spread function. The technique applies to situations in which the scene consists of a finite support object against a uniformly black, grey, or white background. This occurs in certain types of astronomical imaging, medical imaging, and onedimensional (1D) gamma ray spectra processing, among others. The only information required are the nonnegativity of the true image and the support size of the original object. The restoration procedure involves recursive filtering of the blurred image to minimize a convex cost function. We prove convexity of the cost function, establish sufficient conditions to guarantee a unique solution, and examine the performance of the technique in the presence of noise. The new approach is experimentally shown to be more reliable and to have faster convergence than existing nonparametric finite support blind deconvolution methods. For situations in which the exact object support is unknown, we propose a novel supportfinding algorithm.
H.: Progressive interscale and intrascale nonblind image deconvolution
 In ACM SIGGRAPH
, 2008
"... et al. 2006]), standard RichardsonLucy (RL) [Lucy 1974] result, and our result. Abstract. Ringing is the most disturbing artifact in the image deconvolution. In this paper, we present a progressive interscale and intrascale nonblind image deconvolution approach that significantly reduces ringing ..."
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Cited by 56 (2 self)
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et al. 2006]), standard RichardsonLucy (RL) [Lucy 1974] result, and our result. Abstract. Ringing is the most disturbing artifact in the image deconvolution. In this paper, we present a progressive interscale and intrascale nonblind image deconvolution approach that significantly reduces ringing. Our approach is built on a novel edgepreserving deconvolution algorithm called bilateral RichardsonLucy (BRL) which uses a large spatial support to handle large blur. We progressively recover the image from a coarse scale to a fine scale (interscale), and progressively restore image details within every scale (intrascale). To perform the interscale deconvolution, we propose a joint bilateral RichardsonLucy (JBRL) algorithm so that the recovered image in one scale can guide the deconvolution in the next scale. In each scale, we propose an iterative residual deconvolution to progressively recover image details. The experimental results show that our progressive deconvolution can produce images with very little ringing for large blur kernels. 1
Blind motion deblurring using image statistics
 In Advances in Neural Information Processing Systems (NIPS
"... We address the problem of blind motion deblurring from a single image, caused by a few moving objects. In such situations only part of the image may be blurred, and the scene consists of layers blurred in different degrees. Most of of existing blind deconvolution research concentrates at recovering ..."
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Cited by 51 (2 self)
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We address the problem of blind motion deblurring from a single image, caused by a few moving objects. In such situations only part of the image may be blurred, and the scene consists of layers blurred in different degrees. Most of of existing blind deconvolution research concentrates at recovering a single blurring kernel for the entire image. However, in the case of different motions, the blur cannot be modeled with a single kernel, and trying to deconvolve the entire image with the same kernel will cause serious artifacts. Thus, the task of deblurring needs to involve segmentation of the image into regions with different blurs. Our approach relies on the observation that the statistics of derivative filters in images are significantly changed by blur. Assuming the blur results from a constant velocity motion, we can limit the search to one dimensional box filter blurs. This enables us to model the expected derivatives distributions as a function of the width of the blur kernel. Those distributions are surprisingly powerful in discriminating regions with different blurs. The approach produces convincing deconvolution results on real world images with rich texture. 1
Multichannel blind iterative image restoration
 IEEE Trans. Image Processing
, 2003
"... Abstract—Blind image deconvolution is required in many applications of microscopy imaging, remote sensing, and astronomical imaging. Unfortunately in a singlechannel framework, serious conceptual and numerical problems are often encountered. Very recently, an eigenvectorbased method (EVAM) was p ..."
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Cited by 45 (6 self)
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Abstract—Blind image deconvolution is required in many applications of microscopy imaging, remote sensing, and astronomical imaging. Unfortunately in a singlechannel framework, serious conceptual and numerical problems are often encountered. Very recently, an eigenvectorbased method (EVAM) was proposed for a multichannel framework which determines perfectly convolution masks in a noisefree environment if channel disparity, called coprimeness, is satisfied. We propose a novel iterative algorithm based on recent anisotropic denoising techniques of total variation and a Mumford–Shah functional with the EVAM restoration condition included. A linearization scheme of halfquadratic regularization together with a cellcentered finite difference discretization scheme is used in the algorithm and provides a unified approach to the solution of total variation or Mumford–Shah. The algorithm performs well even on very noisy images and does not require an exact estimation of mask orders. We demonstrate capabilities of the algorithm on synthetic data. Finally, the algorithm is applied to defocused images taken with a digital camera and to data from astronomical groundbased observations of the Sun. Index Terms—Conjugate gradient, halfquadratic regularization, multichannel blind deconvolution, Mumford–Shah functional, subspace methods, total variation. I.
Efficient generalized crossvalidation with applications to parametric image restoration and resolution enhancement
 IEEE Trans. Image Processing
, 2001
"... Abstract—In many image restoration/resolution enhancement applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or is known only to within a set of parameters. We estimate these PSF parameters for this illposed class of inverse problem from raw da ..."
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Cited by 41 (7 self)
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Abstract—In many image restoration/resolution enhancement applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or is known only to within a set of parameters. We estimate these PSF parameters for this illposed class of inverse problem from raw data, along with the regularization parameters required to stabilize the solution, using the generalized crossvalidation method (GCV). We propose efficient approximation techniques based on the Lanczos algorithm and Gauss quadrature theory, reducing the computational complexity of the GCV. Datadriven PSF and regularization parameter estimation experiments with synthetic and real image sequences are presented to demonstrate the effectiveness and robustness of our method. Index Terms—Blind restoration, blur identification, generalized crossvalidation, quadrature rules, superresolution. I.
Regularized Constrained Total LeastSquares Image Restoration
 IEEE Trans. Image Processing
, 1995
"... In this paper the problem of restoring an image distorted by a linear spaceinvariant (LSI) pointspread function (psf) which is not exactly known is formulated as the solution of a perturbed set of linear equations. The regularized constrained total leastsquares (RCTLS) method is used to solve thi ..."
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Cited by 33 (7 self)
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In this paper the problem of restoring an image distorted by a linear spaceinvariant (LSI) pointspread function (psf) which is not exactly known is formulated as the solution of a perturbed set of linear equations. The regularized constrained total leastsquares (RCTLS) method is used to solve this set of equations. Using the diagonalization properties of the discrete Fourier transform (DFT) for circulant matrices, the RCTLS estimate is computed in the DFT domain. This significantly reduces the computational cost of this approach and makes its implementation possible even for large images. An error analysis of the RCTLS estimate, based on the meansquarederror (MSE) criterion is performed to verify its superiority over the constrained total leastsquares (CTLS) estimate. Numerical experiments for different psf errors are performed to test the RCTLS estimator for this problem. Objective and visual comparisons are presented with the linear minimum meansquarederror (LMMSE) and the re...
Constrained total least squares computation for high resolution image reconstruction with mulisensors
 International Journal of Systems and Technologies
"... ABSTRACT: Multiple undersampled images of a scene are often obtained by using a chargecoupled device (CCD) detector array of sensors that are shifted relative to each other by subpixel displacements. This geometry of sensors, where each sensor has a subarray of sensing elements of suitable size, h ..."
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Cited by 26 (2 self)
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ABSTRACT: Multiple undersampled images of a scene are often obtained by using a chargecoupled device (CCD) detector array of sensors that are shifted relative to each other by subpixel displacements. This geometry of sensors, where each sensor has a subarray of sensing elements of suitable size, has been popular in the task of attaining spatial resolution enhancement from the acquired lowresolution degraded images that comprise the set of observations. With the objective of improving the performance of the signal processing algorithms in the presence of the ubiquitous perturbation errors of displacements around the ideal subpixel locations (because of imperfections in fabrication), in addition to noisy observation, the errorsinvariables or the total leastsquares method is used in this paper. A regularized constrained total leastsquares (RCTLS) solution to the problem is given, which requires the minimization of a nonconvex and nonlinear cost functional. Simulations indicate that the choice of the regularization parameter influences significantly the quality of the solution. The Lcurve method is used to select the theoretically optimum value of the regularization parameter instead of the unsound but expedient trialanderror approach. The expected superiority of this RCTLS approach over the conventional leastsquares theorybased
Recognition Of Images Degraded By Linear Motion Blur Without Restoration
 Computing Suppl
, 1996
"... The paper is devoted to the featurebased description of images degraded by linear motion blur. The proposed features are invariant with respect to motion velocity, are based on image moments and are calculated directly from the blurred image. In that way, we are able to describe the original image ..."
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Cited by 19 (6 self)
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The paper is devoted to the featurebased description of images degraded by linear motion blur. The proposed features are invariant with respect to motion velocity, are based on image moments and are calculated directly from the blurred image. In that way, we are able to describe the original image without the PSF identification and image restoration. In many applications (such as in image recognition against a database) our approach is much more effective than the traditional "blindrestoration" one. The derivation of the motion blur invariants is a major theoretical result of the paper. Numerical experiments are presented to illustrate the utilization of the invariants for blurred image description. Stability of the invariants with respect to additive random noise is also discussed and is shown to be sufficiently high. Finally, another set of features which are invariant not only to motion velocity but also to motion direction is introduced. Index Terms: Blurred image, linear imaging...