WAVELET CHARACTERIZATION OF HARDY SPACE H<sup>1</sup> AND ITS APPLICATION IN VARIATIONAL IMAGE DECOMPOSITION

Zhang, Tao; Fan, Qing‐Hua; Gao, Qiuli

doi:10.1142/s0219691310003390

Cited by 3 publications

(6 citation statements)

References 27 publications

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“…In [20], [23], we give the discrete wavelet representation of dyadic H 1 norm and dyadic BMO norm, which can be described as the following.…”

Section: Norm and Bmo D Normmentioning

confidence: 99%

“…In our previous work [20], we gave the wavelet characterization of dyadic Hardy norm, and applied model (9) in image decomposition for the first time. But at that time, we did not figure out the mechanism of dyadic Hardy space for texture preserving image restoration.…”

Section: Introductionmentioning

confidence: 99%

“…But at that time, we did not figure out the mechanism of dyadic Hardy space for texture preserving image restoration. In [20], we solved the model in wavelet domain by Nelder-Mead algorithm, which is a simplex method for finding a local minimizer fo a function of several variables. Nelder-Mead algorithm has several drawbacks: it did not make use of derivative information and the performance of the algorithm has a remarkably dependence on the initial simplex.…”

Section: Introductionmentioning

confidence: 99%

“…Nelder-Mead algorithm has several drawbacks: it did not make use of derivative information and the performance of the algorithm has a remarkably dependence on the initial simplex. For these problems of [20], on the one hand, we will give the mechanism of H 1 d space for modeling the oscillating component of the image in Section III A. On the other hand, we will give an efficient algorithm for solving model (9) based on fixed point iteration method in Section III B.…”

Section: Introductionmentioning

confidence: 99%

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Image Restoration Models Based on Dyadic Hardy Space and Dyadic Bounded Mean Oscillation Space

Zhang

2019

IEEE Access

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Texture is widely existed in various images and plays an important role in many area such as medical image diagnosis, remote sensing, etc. However, the image in texture regions is tend to be deteriorated during restoration process. In this paper, we apply the dyadic Hardy space H 1 d and dyadic Bounded Mean Oscillation (BMO) space in the texture preserving image restoration model. We propose a H 1 d regularized minimization model to extract texture from noisy data. In this model, H 1 d norm is taken as regularizer to enforce the prior that the local variance of the noise is below certain level depending on the regularization parameter. We also analyze the mathematical properties of this model which indicate the mechanism of H 1 d regularizer to control the local variance. For the numerical solution of the model, we transform it into wavelet domain based on the wavelet characterization of dyadic Hardy space and dyadic BMO space, and solve it by the fixed iteration algorithm. Combing the total variation (TV) regularization method and frame based regularization method, a two-layers regularization model is proposed for edge and texture preserving, and then analyzed and solved in the frame of split Bregman method. Finally, we present various numerical results on images to demonstrate the potential of our methods.

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“…In [20], [23], we give the discrete wavelet representation of dyadic H 1 norm and dyadic BMO norm, which can be described as the following.…”

Section: Norm and Bmo D Normmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Image Restoration Models Based on Dyadic Hardy Space and Dyadic Bounded Mean Oscillation Space

Zhang

2019

IEEE Access

Self Cite

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“…Wavelet transform plays an important role in image processing, pattern recognition, document analyses, and so forth [1][2][3][4][5][6][7][8][9][10][11][12]. The basic operation of it, in fact, is a linear convolution.…”

Section: Introductionmentioning

confidence: 99%

Implementation of 2D Discrete Wavelet Transform by Number Theoretic Transform and 2D Overlap‐Save Method

Yang

Tang

Sun

2014

Mathematical Problems in Engineering

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To reduce the computation complexity of wavelet transform, this paper presents a novel approach to be implemented. It consists of two key techniques: (1) fast number theoretic transform(FNTT) In the FNTT, linear convolution is replaced by the circular one. It can speed up the computation of 2D discrete wavelet transform. (2) In two-dimensional overlap-save method directly calculating the FNTT to the whole input sequence may meet two difficulties; namely, a big modulo obstructs the effective implementation of the FNTT and a long input sequence slows the computation of the FNTT down. To fight with such deficiencies, a new technique which is referred to as 2D overlap-save method is developed. Experiments have been conducted. The fast number theoretic transform and 2D overlap-method have been used to implement the dyadic wavelet transform and applied to contour extraction in pattern recognition.

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Multiple Component Predictive Coding of Images

Peng

Hwang

2013

Int. J. Wavelets Multiresolut Inf. Process.

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The conventional multiple component image compression approach separates the input image into several components, each of which is predicted and encoded independently. This approach creates redundancy because the prediction methods as well as the residual subcomponents must be transmitted. In this paper, we propose a new multiple-component predictive coding framework. First, we separate the reconstructed image into several subcomponents. Then, we use the previously encoded subcomponent to predict the current block, and then combine the prediction residuals of each subcomponent. To separate an image into multiple subcomponents, we designed a fast operator-based image separation algorithm. The numerical results demonstrate that the algorithm outperforms the H.264/AVC intra-frame prediction algorithm and the JPEG2000 algorithm on images with ample textures.

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WAVELET CHARACTERIZATION OF HARDY SPACE H¹ AND ITS APPLICATION IN VARIATIONAL IMAGE DECOMPOSITION

Cited by 3 publications

References 27 publications

Image Restoration Models Based on Dyadic Hardy Space and Dyadic Bounded Mean Oscillation Space

Image Restoration Models Based on Dyadic Hardy Space and Dyadic Bounded Mean Oscillation Space

Implementation of 2D Discrete Wavelet Transform by Number Theoretic Transform and 2D Overlap‐Save Method

Multiple Component Predictive Coding of Images

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WAVELET CHARACTERIZATION OF HARDY SPACE H1 AND ITS APPLICATION IN VARIATIONAL IMAGE DECOMPOSITION

Cited by 3 publications

References 27 publications

Image Restoration Models Based on Dyadic Hardy Space and Dyadic Bounded Mean Oscillation Space

Image Restoration Models Based on Dyadic Hardy Space and Dyadic Bounded Mean Oscillation Space

Implementation of 2D Discrete Wavelet Transform by Number Theoretic Transform and 2D Overlap‐Save Method

Multiple Component Predictive Coding of Images

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Product

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WAVELET CHARACTERIZATION OF HARDY SPACE H¹ AND ITS APPLICATION IN VARIATIONAL IMAGE DECOMPOSITION