Results 1  10
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159
Algorithms for Nonnegative Matrix Factorization
 In NIPS
, 2001
"... Nonnegative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minim ..."
Abstract

Cited by 721 (4 self)
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Nonnegative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized KullbackLeibler divergence. The monotonic convergence of both algorithms can be proven using an auxiliary function analogous to that used for proving convergence of the ExpectationMaximization algorithm. The algorithms can also be interpreted as diagonally rescaled gradient descent, where the rescaling factor is optimally chosen to ensure convergence.
Removing camera shake from a single photograph
 ACM Trans. Graph
, 2006
"... Camera shake during exposure leads to objectionable image blur and ruins many photographs. Conventional blind deconvolution methods typically assume frequencydomain constraints on images, or overly simplified parametric forms for the motion path during camera shake. Real camera motions can follow c ..."
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Cited by 188 (13 self)
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Camera shake during exposure leads to objectionable image blur and ruins many photographs. Conventional blind deconvolution methods typically assume frequencydomain constraints on images, or overly simplified parametric forms for the motion path during camera shake. Real camera motions can follow convoluted paths, and a spatial domain prior can better maintain visually salient image characteristics. We introduce a method to remove the effects of camera shake from seriously blurred images. The method assumes a uniform camera blur over the image and negligible inplane camera rotation. In order to estimate the blur from the camera shake, the user must specify an image region without saturation effects. We show results for a variety of digital photographs taken from personal photo collections.
Nonlinear Image Recovery with HalfQuadratic Regularization
, 1993
"... One popular method for the recovery of an ideal intensity image from corrupted or indirect measurements is regularization: minimize an objective function which enforces a roughness penalty in addition to coherence with the data. Linear estimates are relatively easy to compute but generally introduce ..."
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Cited by 132 (0 self)
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One popular method for the recovery of an ideal intensity image from corrupted or indirect measurements is regularization: minimize an objective function which enforces a roughness penalty in addition to coherence with the data. Linear estimates are relatively easy to compute but generally introduce systematic errors; for example, they are incapable of recovering discontinuities and other important image attributes. In contrast, nonlinear estimates are more accurate, but often far less accessible. This is particularly true when the objective function is nonconvex and the distribution of each data component depends on many image components through a linear operator with broad support. Our approach is based on an auxiliary array and an extended objective function in which the original variables appear quadratically and the auxiliary variables are decoupled. Minimizing over the auxiliary array alone yields the original function, so the original image estimate can be obtained by joint min...
Coded Exposure Photography: Motion Deblurring using a Fluttered Shutter
 In Proceedings of SIGGRAPH 2006
"... In a conventional singleexposure photograph, moving objects or moving cameras cause motion blur. The exposure time defines a temporal box filter that smears the moving object across the image by convolution. This box filter destroys important highfrequency spatial details so that deblurring via de ..."
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Cited by 110 (18 self)
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In a conventional singleexposure photograph, moving objects or moving cameras cause motion blur. The exposure time defines a temporal box filter that smears the moving object across the image by convolution. This box filter destroys important highfrequency spatial details so that deblurring via deconvolution becomes an illposed problem. Rather than leaving the shutter open for the entire exposure duration, we ¨flutter¨the camera´s shutter open and closed during the chosen exposure time with a binary pseudorandom sequence. The flutter changes the box filter to a broadband filter that preserves highfrequency spatial details in the blurred image and the corresponding deconvolution becomes a wellposed problem. We demonstrate that manuallyspecified point spread functions are sufficient for several challenging cases of motionblur removal including extremely large motions, textured backgrounds and partial occluders. ACM Transactions o Graphics (TOG)
Dappled photography: Mask enhanced cameras for heterodyned light fields and coded aperture refocusing
 in Proc. ACM SIGGRAPH
, 2007
"... Figure 1: Our heterodyne light field camera provides 4D light field and fullresolution focused image simultaneously. (First Column) Raw sensor image. (Second Column) Scene parts which are infocus can be recovered at full resolution. (Third Column) Inset shows finescale light field encoding (top) ..."
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Cited by 93 (21 self)
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Figure 1: Our heterodyne light field camera provides 4D light field and fullresolution focused image simultaneously. (First Column) Raw sensor image. (Second Column) Scene parts which are infocus can be recovered at full resolution. (Third Column) Inset shows finescale light field encoding (top) and the corresponding part of the recovered full resolution image (bottom). (Last Column) Far focused and near focused images obtained from the light field. We describe a theoretical framework for reversibly modulating 4D light fields using an attenuating mask in the optical path of a lens based camera. Based on this framework, we present a novel design to reconstruct the 4D light field from a 2D camera image without any additional refractive elements as required by previous light field cameras. The patterned mask attenuates light rays inside the camera instead of bending them, and the attenuation recoverably encodes the rays on the 2D sensor. Our maskequipped camera focuses just as a traditional camera to capture conventional 2D photos at full sensor resolution, but the raw pixel values also hold a modulated
Image Deblurring with Blurred/Noisy Image Pairs
"... (with shutter speed of 1/100 second, and ISO 1600) due to insufficient light. (c) Noisy image enhanced by adjusting level and gamma. (d) Our deblurred image. Abstract Taking satisfactory photos under dim lighting conditions using a handheld camera is challenging. If the camera is set to a long expo ..."
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Cited by 84 (4 self)
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(with shutter speed of 1/100 second, and ISO 1600) due to insufficient light. (c) Noisy image enhanced by adjusting level and gamma. (d) Our deblurred image. Abstract 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. 1
Platelets: A Multiscale Approach for Recovering Edges and Surfaces in PhotonLimited Medical Imaging
 IEEE TRANSACTIONS ON MEDICAL IMAGING
, 2003
"... The nonparametric multiscale platelet algorithms presented in this paper, unlike traditional waveletbased methods, are both well suited to photonlimited medical imaging applications involving Poisson data and capable of better approximating edge contours. This paper introduces platelets, localized ..."
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Cited by 77 (19 self)
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The nonparametric multiscale platelet algorithms presented in this paper, unlike traditional waveletbased methods, are both well suited to photonlimited medical imaging applications involving Poisson data and capable of better approximating edge contours. This paper introduces platelets, localized functions at various scales, locations, and orientations that produce piecewise linear image approximations, and a new multiscale image decomposition based on these functions. Platelets are well suited for approximating images consisting of smooth regions separated by smooth boundaries. For smoothness measured in certain H older classes, it is shown that the error of mterm platelet approximations can decay significantly faster than that of mterm approximations in terms of sinusoids, wavelets, or wedgelets. This suggests that platelets may outperform existing techniques for image denoising and reconstruction. Fast, plateletbased, maximum penalized likelihood methods for photonlimited image denoising, deblurring and tomographic reconstruction problems are developed. Because platelet decompositions of Poisson distributed images are tractable and computationally efficient, existing image reconstruction methods based on expectationmaximization type algorithms can be easily enhanced with platelet techniques. Experimental results suggest that plateletbased methods can outperform standard reconstruction methods currently in use in confocal microscopy, image restoration, and emission tomography.
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 42 (3 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
Multiresolution Support Applied to Image Filtering and Restoration
, 1995
"... The notion of a multiresolution support is introduced. This is a sequence of boolean images, related to significant pixels at each of a number of resolution levels. The multiresolution support is then used for noise suppression, in the context of image filtering, or iterative image restoration. A ..."
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Cited by 39 (21 self)
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The notion of a multiresolution support is introduced. This is a sequence of boolean images, related to significant pixels at each of a number of resolution levels. The multiresolution support is then used for noise suppression, in the context of image filtering, or iterative image restoration. Algorithmic details, and a range of practical examples, illustrate this approach.
Fast Image Deconvolution using HyperLaplacian
"... The heavytailed distribution of gradients in natural scenes have proven effective priors for a range of problems such as denoising, deblurring and superresolution. These distributions are well modeled by a hyperLaplacian ( p(x) ∝ e −kxα) , typically with 0.5 ≤ α ≤ 0.8. However, the use of spar ..."
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Cited by 38 (1 self)
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The heavytailed distribution of gradients in natural scenes have proven effective priors for a range of problems such as denoising, deblurring and superresolution. These distributions are well modeled by a hyperLaplacian ( p(x) ∝ e −kxα) , typically with 0.5 ≤ α ≤ 0.8. However, the use of sparse distributions makes the problem nonconvex and impractically slow to solve for multimegapixel images. In this paper we describe a deconvolution approach that is several orders of magnitude faster than existing techniques that use hyperLaplacian priors. We adopt an alternating minimization scheme where one of the two phases is a nonconvex problem that is separable over pixels. This perpixel subproblem 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. 1