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81
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 ..."
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Cited by 114 (10 self)
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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.
Pointwise shapeadaptive DCT for highquality denoising and deblocking of grayscale and color images
, 2007
"... The shapeadaptive discrete cosine transform (SADCT) transform can be computed on a support of arbitrary shape, but retains a computational complexity comparable to that of the usual separable blockDCT (BDCT). Despite the nearoptimal decorrelation and energy compaction properties, application o ..."
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Cited by 72 (14 self)
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The shapeadaptive discrete cosine transform (SADCT) transform can be computed on a support of arbitrary shape, but retains a computational complexity comparable to that of the usual separable blockDCT (BDCT). Despite the nearoptimal decorrelation and energy compaction properties, application of the SADCT has been rather limited, targeted nearly exclusively to video compression. In this paper, we present a novel approach to image filtering based on the SADCT. We use the SADCT in conjunction with the Anisotropic Local Polynomial Approximation—Intersection of Confidence Intervals technique, which defines the shape of the transform’s support in a pointwise adaptive manner. The thresholded or attenuated SADCT coefficients are used to reconstruct a local estimate of the signal within the adaptiveshape support. Since supports corresponding to different points are in general overlapping, the local estimates are averaged together using adaptive weights that depend on the region’s statistics. This approach can be used for various imageprocessing tasks. In this paper, we consider, in particular, image denoising and image deblocking and deringing from blockDCT compression. A special structural constraint in luminancechrominance space is also proposed to enable an accurate filtering of color images. Simulation experiments show a stateoftheart quality of the final estimate, both in terms of objective criteria and visual appearance. Thanks to the adaptive support, reconstructed edges are clean, and no unpleasant ringing artifacts are introduced by the fitted transform.
Local adaptivity to variable smoothness for exemplarbased image denoising and representation
, 2005
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A New Method for Varying Adaptive Bandwidth Selection
 IEEE Trans. on Signal Proc
, 1999
"... A novel approach is developed to solve a problem of varying bandwidth selection for filtering a signal given with an additive noise. The approach is based on the intersection of confidence intervals (ICI) rule and gives the algorithm, which is simple to implement and adaptive to unknown smoothness o ..."
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Cited by 47 (24 self)
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A novel approach is developed to solve a problem of varying bandwidth selection for filtering a signal given with an additive noise. The approach is based on the intersection of confidence intervals (ICI) rule and gives the algorithm, which is simple to implement and adaptive to unknown smoothness of the signal.
Estimation Of A Function With Discontinuities Via Local Polynomial Fit With An Adaptive Window Choice
, 1996
"... . We propose a method of adaptive estimation of a regression function and which is near optimal in the classical sense of the mean integrated error. At the same time, the estimator is shown to be very sensitive to discontinuities or changepoints of the underlying function f or its derivatives. For ..."
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Cited by 42 (4 self)
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. We propose a method of adaptive estimation of a regression function and which is near optimal in the classical sense of the mean integrated error. At the same time, the estimator is shown to be very sensitive to discontinuities or changepoints of the underlying function f or its derivatives. For instance, in the case of a jump of a regression function, beyond the interval of length (in order) n \Gamma1 log n around changepoints the quality of estimation is essentially the same as if locations of jumps were known. The method is fully adaptive and no assumptions are imposed on the design, number and size of jumps. The results are formulated in a nonasymptotic way and can be therefore applied for an arbitrary sample size. 1. Introduction The changepoint analysis which includes sudden, localized changes typically occurring in economics, medicine and the physical sciences has recently found increasing interest, see Muller (1992) for some examples and discussion of the problem. Let...
On Pointwise Adaptive Nonparametric Deconvolution
 Bernoulli
, 1998
"... We consider estimating an unknown function f from indirect white noise observations with particular emphasis on the problem of nonparametric deconvolution. Nonparametric estimators that can adapt to unknown smoothness of f are developed. The adaptive estimators are specified under two sets of assump ..."
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Cited by 29 (3 self)
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We consider estimating an unknown function f from indirect white noise observations with particular emphasis on the problem of nonparametric deconvolution. Nonparametric estimators that can adapt to unknown smoothness of f are developed. The adaptive estimators are specified under two sets of assumptions on the kernel of the convolution transform. In particular, kernels having the Fourier transform with polynomially and exponentially decaying tails are considered. It is shown that the proposed estimates possess, in a sense, the best possible abilities for pointwise adaptation. Keywords: adaptive estimation; deconvolution; rates of convergence Running title: Adaptive nonparametric deconvolution Department of Statistics, University of Haifa, Mount Carmel, 31905 Haifa, Israel y email: goldensh@rstat.haifa.ac.il 1 Introduction This paper investigates the problem of pointwise adaptive nonparametric estimation from indirect white noise observations. Let f 2 L 2 (R) be an unknown func...
A spatially adaptive nonparametric regression image deblurring
 IEEE TRANS. IMAGE PROCESS
, 2005
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On minimax density estimation on R
 Bernoulli
, 2004
"... Abstract: the problem of density estimation on R from an independent sample X1,...XN with common density f is concerned. The behavior of the minimax Lprisk, 1 ≤ p ≤ ∞, is studied when f belongs to a Hölder class of regularity s on the real line. The lower bound for the minimax risk is provided. We ..."
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Cited by 21 (0 self)
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Abstract: the problem of density estimation on R from an independent sample X1,...XN with common density f is concerned. The behavior of the minimax Lprisk, 1 ≤ p ≤ ∞, is studied when f belongs to a Hölder class of regularity s on the real line. The lower bound for the minimax risk is provided. We show that the linear estimator is not efficient in this setting and construct a wavelet adaptive estimator which attains (up to a logarithmic factor in N) the lower bounds involved. We show that the minimax risk depends on the parameter p when p < 2 + 1 s. Key words: nonparametric density estimation, minimax estimation, adaptive estimation. 1