Results 11  20
of
513
Kernel regression for image processing and reconstruction
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2007
"... In this paper, we make contact with the field of nonparametric statistics and present a development and generalization of tools and results for use in image processing and reconstruction. In particular, we adapt and expand kernel regression ideas for use in image denoising, upscaling, interpolation, ..."
Abstract

Cited by 172 (53 self)
 Add to MetaCart
In this paper, we make contact with the field of nonparametric statistics and present a development and generalization of tools and results for use in image processing and reconstruction. In particular, we adapt and expand kernel regression ideas for use in image denoising, upscaling, interpolation, fusion, and more. Furthermore, we establish key relationships with some popular existing methods and show how several of these algorithms, including the recently popularized bilateral filter, are special cases of the proposed framework. The resulting algorithms and analyses are amply illustrated with practical examples.
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 ..."
Abstract

Cited by 130 (4 self)
 Add to MetaCart
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.
EMPIRICAL BAYES SELECTION OF WAVELET THRESHOLDS
, 2005
"... This paper explores a class of empirical Bayes methods for leveldependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavytailed density. The mixing weight, or sparsity parameter, for each level of ..."
Abstract

Cited by 117 (5 self)
 Add to MetaCart
This paper explores a class of empirical Bayes methods for leveldependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavytailed density. The mixing weight, or sparsity parameter, for each level of the transform is chosen by marginal maximum likelihood. If estimation is carried out using the posterior median, this is a random thresholding procedure; the estimation can also be carried out using other thresholding rules with the same threshold. Details of the calculations needed for implementing the procedure are included. In practice, the estimates are quick to compute and there is software available. Simulations on the standard model functions show excellent performance, and applications to data drawn from various fields of application are used to explore the practical performance of the approach. By using a general result on the risk of the corresponding marginal maximum likelihood approach for a single sequence, overall bounds on
Why simple shrinkage is still relevant for redundant representations
 IEEE Trans. Inf. Theory
, 2006
"... General Description • Problem statement: Shrinkage is a well known and appealing denoising technique, introduced originally by Donoho and Johnstone in 1994. The use of shrinkage for denoising is known to be optimal for Gaussian white noise, provided that the sparsity on the signal's representa ..."
Abstract

Cited by 115 (12 self)
 Add to MetaCart
(Show Context)
General Description • Problem statement: Shrinkage is a well known and appealing denoising technique, introduced originally by Donoho and Johnstone in 1994. The use of shrinkage for denoising is known to be optimal for Gaussian white noise, provided that the sparsity on the signal's representation is enforced using a unitary transform. Still, shrinkage is also practiced with nonunitary, and even redundant representations, typically leading to satisfactory results. In this paper we shed some light on this behavior. • Originality of the work: The main argument in this paper is that such simple shrinkage could be interpreted as the first iteration of an algorithm that solves the basis pursuit denoising (BPDN) problem. While the desired solution of BPDN is hard to obtain in general, a simple iterative procedure that amounts to stepwise shrinkage can be employed with quite successful performance. • New results: We demonstrate how the simple shrinkage emerges as the first iteration of such algorithm. Furthermore, we show how shrinkage can be iterated, turning into an effective algorithm that minimizes the BPDN via simple shrinkage steps, in order to further strengthen the denoising effect. Lastly, the emerging algorithm stands in between the basis and the matching pursuit as a novel and appealing pursuit technique for atom decomposition in the presence of noise.
Optimal spatial adaptation for patchbased image denoising
 IEEE Trans. Image Process
, 2006
"... Abstract—A novel adaptive and patchbased approach is proposed for image denoising and representation. The method is based on a pointwise selection of small image patches of fixed size in the variable neighborhood of each pixel. Our contribution is to associate with each pixel the weighted sum of da ..."
Abstract

Cited by 113 (10 self)
 Add to MetaCart
(Show Context)
Abstract—A novel adaptive and patchbased approach is proposed for image denoising and representation. The method is based on a pointwise selection of small image patches of fixed size in the variable neighborhood of each pixel. Our contribution is to associate with each pixel the weighted sum of data points within an adaptive neighborhood, in a manner that it balances the accuracy of approximation and the stochastic error, at each spatial position. This method is general and can be applied under the assumption that there exists repetitive patterns in a local neighborhood of a point. By introducing spatial adaptivity, we extend the work earlier described by Buades et al. which can be considered as an extension of bilateral filtering to image patches. Finally, we propose a nearly parameterfree algorithm for image denoising. The method is applied to both artificially corrupted (white Gaussian noise) and real images and the performance is very close to, and in some cases even surpasses, that of the already published denoising methods. I.
Fast image deconvolution using hyperlaplacian priors, supplementary material
, 2009
"... 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 ..."
Abstract

Cited by 109 (2 self)
 Add to MetaCart
(Show Context)
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
Learning multiscale sparse representations for image and video restoration
, 2007
"... Abstract. This paper presents a framework for learning multiscale sparse representations of color images and video with overcomplete dictionaries. A singlescale KSVD algorithm was introduced in [1], formulating sparse dictionary learning for grayscale image representation as an optimization proble ..."
Abstract

Cited by 103 (21 self)
 Add to MetaCart
(Show Context)
Abstract. This paper presents a framework for learning multiscale sparse representations of color images and video with overcomplete dictionaries. A singlescale KSVD algorithm was introduced in [1], formulating sparse dictionary learning for grayscale image representation as an optimization problem, efficiently solved via Orthogonal Matching Pursuit (OMP) and Singular Value Decomposition (SVD). Following this work, we propose a multiscale learned representation, obtained by using an efficient quadtree decomposition of the learned dictionary, and overlapping image patches. The proposed framework provides an alternative to predefined dictionaries such as wavelets, and shown to lead to stateoftheart results in a number of image and video enhancement and restoration applications. This paper describes the proposed framework, and accompanies it by numerous examples demonstrating its strength. Key words. Image and video processing, sparsity, dictionary, multiscale representation, denoising, inpainting, interpolation, learning. AMS subject classifications. 49M27, 62H35
NONSUBSAMPLED CONTOURLET TRANSFORM: FILTER DESIGN AND APPLICATIONS IN DENOISING
"... In this paper we study the nonsubsampled contourlet transform. We address the corresponding filter design problem using the McClellan transformation. We show how zeroes can be imposed in the filters so that the iterated structure produces regular basis functions. The proposed design framework yields ..."
Abstract

Cited by 101 (4 self)
 Add to MetaCart
(Show Context)
In this paper we study the nonsubsampled contourlet transform. We address the corresponding filter design problem using the McClellan transformation. We show how zeroes can be imposed in the filters so that the iterated structure produces regular basis functions. The proposed design framework yields filters that can be implemented efficiently through a lifting factorization. We apply the constructed transform in image noise removal where the results obtained are comparable to the stateofthe art, being superior in some cases.
What makes a good model of natural images
 in: CVPR 2007: Proceedings of the 2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE Computer Society
, 2007
"... ..."
(Show Context)
Directional Multiscale Modeling of Images using the Contourlet Transform
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2004
"... The contourlet transform is a new extension to the wavelet transform in two dimensions using nonseparable and directional filter banks. The contourlet expansion is composed of basis images oriented at varying directions in multiple scales, with flexible aspect ratios. With this rich set of basis ima ..."
Abstract

Cited by 90 (5 self)
 Add to MetaCart
The contourlet transform is a new extension to the wavelet transform in two dimensions using nonseparable and directional filter banks. The contourlet expansion is composed of basis images oriented at varying directions in multiple scales, with flexible aspect ratios. With this rich set of basis images, the contourlet transform can effectively capture the smooth contours that are the dominant features in natural images with only a small number of coefficients. We begin with a detailed study on the statistics of the contourlet coefficients of natural images, using histogram estimates of the marginal and joint distributions, and mutual information measurements to characterize the dependencies between coefficients. The study reveals the nonGaussian marginal statistics and strong intrasubband, crossscale, and crossorientation dependencies of contourlet coefficients. It is also found that conditioned on the magnitudes of their generalized neighborhood coefficients, contourlet coefficients can approximately be modeled as Gaussian variables. Based on these statistics, we model contourlet coefficients using a hidden Markov tree (HMT) model that can capture all of their interscale, interorientation, and intrasubband dependencies. We experiment this model in the image denoising and texture retrieval applications where the results are very promising. In denoising, contourlet HMT outperforms wavelet HMT and other classical methods in terms of visual quality. In particular, it preserves edges and oriented features better than other existing methods. In texture retrieval, it shows improvements in performance over wavelet methods for various oriented textures.