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19
Waveletbased deconvolution for illconditioned systems. Submitted to
 Deparment of Electrical and Computer Engineering, Rice University
"... In this paper, we propose a new approach to waveletbased deconvolution. Roughly speaking, the algorithm comprises Fourierdomain system inversion followed by waveletdomain noise suppression. Our approach subsumes a number of other waveletbased deconvolution methods. In contrast to other wavelet ..."
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Cited by 28 (4 self)
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In this paper, we propose a new approach to waveletbased deconvolution. Roughly speaking, the algorithm comprises Fourierdomain system inversion followed by waveletdomain noise suppression. Our approach subsumes a number of other waveletbased deconvolution methods. In contrast to other waveletbased approaches, however, we employ a regularized inverse filter, which allows the algorithm to operate even when the inverse system is illconditioned or noninvertible. Using a meansquareerror metric, we strike an optimal balance between Fourierdomain and waveletdomain regularization. The result is a fast deconvolution algorithm ideally suited to signals and images with edges and other singularities. In simulations with real data, the algorithm outperforms the LTI Wiener filter and other waveletbased deconvolution algorithms in terms of both visual quality and MSE performance. 1.
Survey of image denoising techniques

"... Removing noise from the original signal is still a challenging problem for researchers. There have been several published algorithms and each approach has its assumptions, advantages, and limitations. This paper presents a review of some significant work in the area of image denoising. After a brief ..."
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Cited by 26 (0 self)
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Removing noise from the original signal is still a challenging problem for researchers. There have been several published algorithms and each approach has its assumptions, advantages, and limitations. This paper presents a review of some significant work in the area of image denoising. After a brief introduction, some popular approaches are classified into different groups and an overview of various algorithms and analysis is provided. Insights and potential future trends in the area of denoising are also discussed.
ECG signal denoising using wavelet domain Wiener filtering
 in Proc. European Signal Processing Conf. EUSIPCO2000
, 2000
"... A twostage algorithm for suppression of electromyogram (EMG) artifacts from the electrocardiogram (ECG) using Wavelet Domain Wiener Filtering has been investigated. An improvement of the traditional technique is proposed by involving Timefrequency dependent threshold for calculation of the pilot ..."
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A twostage algorithm for suppression of electromyogram (EMG) artifacts from the electrocardiogram (ECG) using Wavelet Domain Wiener Filtering has been investigated. An improvement of the traditional technique is proposed by involving Timefrequency dependent threshold for calculation of the pilot estimate in the first stage. The appropriate choice of the wavelet basis functions used in each stage has been stressed. The strong relationship between the wavelet functionâ€™s support and the ECG morphology has been emphasized. The preliminary assumptions have been argued by experiments on a wide range database. They have shown that an appropriate choice of the decomposing wavelets for the two algorithm stages can considerably improve the quality of the denoised signal. 1.
Multiple basis wavelet denoising using besov projections
 In ICIP
, 1999
"... Waveletbased image denoising algorithm depends upon the energy compaction property of wavelet transforms. However, for many realworld images, we cannot expect good energy compaction in a single wavelet domain, because most realworld images consist of components of a variety of smoothness. We can ..."
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Waveletbased image denoising algorithm depends upon the energy compaction property of wavelet transforms. However, for many realworld images, we cannot expect good energy compaction in a single wavelet domain, because most realworld images consist of components of a variety of smoothness. We can relieve this problem by using multiple wavelet bases to match different characteristics of images. In this paper, we propose a novel image denoising algorithm that uses multiple wavelet bases. By establishing a new relationship between the deterministic Besov space theory and the waveletdomain statistical models, we generalize the Besov theory for finite sampled data. After defining convex sets in Besov spaces that contain the true image, we obtain an estimate of the true image by the method of projection onto convex sets. The algorithm outperforms existing multiple wavelet basis denoising algorithms; in particular, it shows excellent performance at low signaltonoise ratios. 1.
WaveletBased Deconvolution Using Optimally Regularized Inversion for IllConditioned Systems
 in Wavelet Applications in Signal and Image Processing VII, Proc. SPIE
, 1999
"... We propose a hybrid approach to waveletbased deconvolution that comprises Fourierdomain system inversion followed by waveletdomain noise suppression. In contrast to conventional waveletbased deconvolution approaches, the algorithm employs a regularized inverse filter, which allows it to operate ..."
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Cited by 6 (3 self)
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We propose a hybrid approach to waveletbased deconvolution that comprises Fourierdomain system inversion followed by waveletdomain noise suppression. In contrast to conventional waveletbased deconvolution approaches, the algorithm employs a regularized inverse filter, which allows it to operate even when the system is noninvertible. Using a meansquareerror (MSE) metric, we strike an optimal balance between Fourierdomain regularization (matched to the system) and waveletdomain regularization (matched to the signal/image). Theoretical analysis reveals that the optimal balance is determined by the economics of the signal representation in the wavelet domain and the operator structure. The resulting algorithm is fast (O(N log 2 2 N) complexity for signals/images of N samples) and is wellsuited to data with spatiallylocalized phenomena such as edges. In addition to enjoying asymptotically optimal rates of error decay for certain systems, the algorithm also achieves excellent per...
Adaptive Algorithm for Image Denoising Based on Curvelet Threshold
 International Journal of Computer Science and Network Security, Vol.10, No.1
, 2010
"... Image Denoising has remained a fundamental problem in the field of image processing. This paper proposes an adaptive threshold method for image denoising based on curvelet transform to estimate noise and remove it from digital images in order to achieve a good performance in this respect. The propos ..."
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Image Denoising has remained a fundamental problem in the field of image processing. This paper proposes an adaptive threshold method for image denoising based on curvelet transform to estimate noise and remove it from digital images in order to achieve a good performance in this respect. The proposed adaptive threshold method is more efficient in estimate and reduce noise from images which have random, salt & pepper and Gaussian noise. Experimental results show that the proposed method demonstrates an improved denoising performance over related earlier techniques according to increasing of PSNR values of enhanced images by 0.044 at Random,1.05 at salt & pepper and 0.457 at Gaussian noise. Key words: Image denoising, Curvelet transform, Image
Spatially Adaptive Wiener Filtering For Image Denoising Using Undecimated Wavelet Transform
, 1999
"... Recently wavelet thresholding has been a popular approach to the 1D and 2D signal (image) denoising. In this work, instead of thresholding the wavelet coefficients, estimation approaches are proposed in the wavelet domain to reduce the noise. The fundamental philosophy is to consider the wavelet c ..."
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Recently wavelet thresholding has been a popular approach to the 1D and 2D signal (image) denoising. In this work, instead of thresholding the wavelet coefficients, estimation approaches are proposed in the wavelet domain to reduce the noise. The fundamental philosophy is to consider the wavelet coefficients as a stationary random signal. Therefore, an optimal linear mean squared error estimate can be obtained from the corrupted observations. It turns out this is the Wiener filtering. In this paper we propose an FIR approximation approach to the IIR Wiener filter and use it in image denoising. Key words Undecimated wavelet transform, autocorrelation function, linear minimum mean squared error estimation 1 Contents 1 Introduction 2 2 Adaptive Wiener filtering 2 2.1 Wiener filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Adaptive Wiener filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Wavelet domain adaptive...
Informationtheoretic Interpretation of Besov Spaces
 In SPIE
, 2000
"... Besov spaces classify signals and images through the Besov norm, which is based on a deterministic smoothness measurement. Recently, we revealed the relationship between the Besov norm and the likelihood of an independent generalized Gaussian wavelet probabilistic model. In this paper, we extend thi ..."
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Besov spaces classify signals and images through the Besov norm, which is based on a deterministic smoothness measurement. Recently, we revealed the relationship between the Besov norm and the likelihood of an independent generalized Gaussian wavelet probabilistic model. In this paper, we extend this result by providing an informationtheoretic interpretation of the Besov norm as the Shannon codelength for signal compression under this probabilistic mode. This perspective unites several seemingly disparate signal/image processing methods, including denoising by Besov norm regularization, complexity regularized denoising, minimum description length (MDL) processing, and maximum smoothness interpolation. By extending the wavelet probabilistic model (to a locally adapted Gaussian model), we broaden the notion of smoothness space to more closely characterize realworld data. The locally Gaussian model leads directly to a powerful waveletdomain Wiener filtering algorithm for denoising. Ke...
WInliD: Waveletbased Inverse Halftoning via Deconvolution
, 2002
"... We propose the Waveletbased Inverse Halftoning via Deconvolution (WInliD) algorithm to perform inverse halftoning of errordiffused halftones. WInliD is motivated by our realization that inverse halftoning can be formulated as a deconvolution problem under Kite et al.'s linear approximation ..."
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We propose the Waveletbased Inverse Halftoning via Deconvolution (WInliD) algorithm to perform inverse halftoning of errordiffused halftones. WInliD is motivated by our realization that inverse halftoning can be formulated as a deconvolution problem under Kite et al.'s linear approximation model for error diffusion halftoning. Under the linear model, the errordiffused halftone comprises the original grayscale image blurred by a convolution operator and colored noise; the convolution operator and noise coloring are determined by the error diffusion tech nique. WInliD performs inverse halftoning by first inverting the modelspecified convolution operator and then attenuating the residual noise using scalar waveletdomain shrinkage. Since WInliD is modelbased, it is easily adapted to different error diffusion halftoning techniques. Using
Wavelet Shrinkage Techniques for Images
"... An image is often corrupted by noise in its acquisition and transmission. Image denoising is used to remove the additive noise while retaining as much as possible the important image features. The motivation is that as wavelet transform is good at energy compaction, the small coefficients are more l ..."
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An image is often corrupted by noise in its acquisition and transmission. Image denoising is used to remove the additive noise while retaining as much as possible the important image features. The motivation is that as wavelet transform is good at energy compaction, the small coefficients are more likely due to noise and large coefficient due to important signal features [6]. The proposed technique is based upon the analysis of wavelet transform which uses a soft thresholding method for thresholding the small coefficients without affecting the significant features of the image. In the proposed work, image denoising is studied using various wavelets for different images with two different noises at various levels of decomposition and comparison is done between the e three methods of wavelet shrinkage techniques.