Modeling curvelet domain inter-band image statistics with application to spatially adaptive image denoising (original) (raw)
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Context adaptive image denoising through modeling of curvelet domain statistics
Journal of Electronic …, 2008
We perform a statistical analysis of curvelet coefficients, distinguishing between two classes of coefficients: those that contain a significant noise-free component, which we call the "signal of interest," and those that do not. By investigating the marginal statistics, we develop a prior model for curvelet coefficients. The analysis of the joint intra-and inter-band statistics enables us to develop an appropriate local spatial activity indicator for curvelets. Finally, based on our findings, we present a novel denoising method, inspired by a recent wavelet domain method called ProbShrink. The new method outperforms its wavelet-based counterpart and produces results that are close to those of state-of-the-art denoisers.
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2006
abstract In this paper, we perform a statistical analysis of curvelet coefficients, making a distinction between two classes of coefficients: those representing useful image content and those dominated by noise. By investigating the marginal statistics, we develop a mixture prior for curvelet coefficients. Through analysis of the joint intra-band statistics, we find that white Gaussian noise is transformed by the curvelet transform into noise that is correlated in one direction and decorrelated in the perpendicular direction.
Proc. SPIE, 2005
We study an image denoising approach the core of which is a locally adaptive estimation of the probability that a given coefficient contains a significant noise-free component, which we call "signal of interest". We motivate this approach within the minimum mean squared error criterion and develop and analyze different locally adaptive versions of this method for color and for multispectral images in remote sensing. For color images, we study two different approaches: (i) using a joint spatial/spectral activity indicator in the RGB color space and (ii) componentwise spatially adaptive denoising in a luminance-chrominance space. We demonstrate and discuss the advantages of both of these approaches in different scenarios. We also compare the analyzed method to other recent wavelet domain denoisers for multiband data both on color and on multispectral images.
2007
This paper proposes a new statistical model for curvelet coefficients of images to characterize both leptokurtic behavior and spatially clustering property of them. We employ a mixture of Gaussian probability density functions (pdfs) with local parameter to model the distribution of noise-free curvelet coefficients. This pdf is mixture and so it is able to model the heavy-tailed nature of curvelet coefficients. Since we use local parameters for mixture model, the proposed pdf can capture the clustering property of curvelet coefficients in spatial adjacent. This model is employed for noise reduction in a Bayesian framework using maximum a posteriori (MAP) estimator. We examine this method for denoising of several grayscale images such as CT image corrupted with additive Gaussian noise in various noise levels. The simulation results show that the proposed method has better performance visually and in terms of peek signal-to-noise ratio (PSNR) from several denoising methods in wavelet and curvelet domain.
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I would like to thank my promotors, Prof. Wilfried Philips and Prof. Marc Acheroy, for following my research with interest and for giving me constant support. I am thankful to Prof. Philips for his many suggestions and positive criticism during my research. Prof. Acheroy gave me a great encouragement and the opportunity to take part in many international conferences.
A 4-quadrant Curvelet Transform for Denoising Digital Images
International Journal of Automation and Computing, 2013
The conventional discrete wavelet transform (DWT) introduces artifacts during denoising of images containing smooth curves. Finite ridgelet transform (FRIT) solved this problem by mapping the curves in terms of small curved ridges. However, blind application of FRIT all over an image is computationally heavy. Finite curvelet transform (FCT) selectively applies FRIT only to the tiles containing small portions of a curve. In this work, a novel curvelet transform named as 4-quadrant finite curvelet transform (4QFCT) based on a new concept of 4-quadrant finite ridgelet transform (4QFRIT) has been proposed. An image is band pass filtered and the high frequency bands are divided into small non-overlapping square tiles. The 4QFRIT is applied to the tiles containing at least one curve element. Unlike FRIT, the 4QFRIT takes 4 sets of radon projections in all the 4 quadrants and then averages them in time and frequency domains after denoising. The proposed algorithm is extensively tested and benchmarked for denoising of images with Gaussian noise using mean squared error (MSE) and peak signal to noise ratio (PSNR). The results confirm that 4QFCT yields consistently better denoising performance quantitatively and visually.
Segmentation Based Combined Wavelet-Curvelet Approach for Image Denoising
International Journal of Information Engineering
This paper presents an efficient image denoising method that adaptively combines the features of wavelets, wave atoms and curvelets. Wavelet shrinkage is used to denoise the smooth regions in the image while wave atoms are employed to denoise the textures, and the edges will take advantage of curvelet denoising. The received noisy image is firstly decomposed into a homogenous (smooth/cartoon) part and a textural part. The cartoon part of the noisy image is denoised using wavelet transform, and the texture part of the noisy image is denoised using wave atoms. The two denoised images are then fused adaptively. For adaptive fusion, different weights are chosen from the variance map of the denoised texture image. Further improvement in denoising results is achieved by denoising the edges through curvelet transform. The information about edge location is gathered from the variance map of denoised cartoon image. The denoised image results in perfect presentation of the smooth regions and efficient preservation of textures and edges in the image.
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Wavelet transform has played an important role in Image processing task such as compression and restoration. Unlike most of existing denoising algorithms, using the curvelet makes it needless to hypothesize a statistical model for the noiseless image. This wavelet transform fails to represent the images, which has edges and treated them as smooth functions with discontinuity along curves. The curvelet transforms, where frame elements are indexed by scale, location and orientation parameters. This curvelet transform is designed to represent edges and other singularities along the curves which are more efficient than the traditional wavelet transform. Moreover, the curvelet transform and Gaussian filter are used for an effective image denoising system. This process will be based on the block-based noise estimation technique, in which an input image will be contaminated by the additive white Gaussian noise and filtering process to be performed by an adaptive Gaussian filter and curvele...
Evaluation of wavelet domain methods for image denoising
Image denoising is a common procedure in digital image processing aiming at the removal of noise, which may corrupt an image during its acquisition or transmission, while retaining its quality. This procedure is traditionally performed in the spatial or frequency domain by filtering. Recently, a lot of methods have been reported that perform denoising on the Discrete Wavelet Transform (DWT) domain. The transform coefficients within the subbands of a DWT can be locally modeled as i.i.d (independent identically distributed) random variables with Generalized Gaussian distribution. Some of the denoising algorithms perform thresholding of the wavelet coefficients, which have been affected by additive white Gaussian noise, by retaining only large coefficients and setting the rest to zero. However, their performance is not sufficiently effective as they are not spatially adaptive. Some other methods evaluate the denoised coefficients by an MMSE (Minimum Mean Square Error) estimator, in terms of the noised coefficients and the variances of signal and noise. The signal variance is locally estimated by a ML (Maximum Likelihood) or a MAP (Maximum A Posteriori) estimator in small regions for every subband where variance is assumed practically constant. These methods present effective results but their spatial adaptivity is not well suited near object edges where the variance field is not smoothly varied. The optimality of the selected regions where the estimators apply has been examined in some research works.
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