Image Denoising Using a New Implementation of the Hyperanalytic Wavelet Transform (original) (raw)
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A Bayesian Approach of Hyperanalytic Wavelet Transform Based Denoising
2007 IEEE International Symposium on Intelligent Signal Processing, 2007
The property of shift-invariance associated with a good directional selectivity is important for the application of a wavelet transform, (WT), in many fields of image processing. Generally, complex wavelet transforms, like for example the Double Tree Complex Wavelet Transform, (DTCWT), have these good properties. In this paper we propose the use of a new implementation of such a WT, recently introduced, namely the hyperanalytic wavelet transform, (HWT), in denoising applications. The proposed denoising method is very simple, implying three steps: the computation of the forward WT, the filtering in the wavelets domain and the computation of the inverse WT, (IWT). The goal of this paper is the association of a new implementation of the HWT, recently proposed, with a maximum a posteriori (MAP) filter. Some simulation examples and comparisons prove the performances of the proposed denoising method.
This paper emphasizes the improvement in the denoising capability of the new proposed technique " Hyperanalytic Dual Tree Complex Wavelet Transform (HDTCWT) ". This technique combines the merits of both Hyperanalytic Wavelet Transform (HWT) and Dual Tree Complex Wavelet Transform (DTCWT). Bi-variate shrinkage Filtering excels in estimating the signal from the noisy signals. The proposed wavelet transform performs better than the HWT and DTCWT based image denoising techniques.
A new implementation of the hyperanalytic wavelet transform
ISSCS 2007 - International Symposium on Signals, Circuits and Systems, Proceedings, 2007
The property of shift-invariance associated with a good directional selectivity are important for the application of a wavelet transform in many fields of image processing. Unfortunately, the 2D discrete wavelet transform is shift-variant and has a reduced directional selectivity. These disadvantages can be attenuated if a complex wavelet transform is used. In this paper, we propose a new implementation of such a wavelet transform, recently introduced, the hyperanalytic wavelet transform. It is quasi shift-invariant, it has a good directional selectivity, and a reduced degree of redundancy of 4 in 2D. The implementation proposed is very simple.
In this paper we propose the use of a new implementation of the hyperanalytic wavelet transform, (HWT), in association with a Maximum a Posteriori (MAP) filter named bishrink. Such a denoising method is sensitive to the selection of the mother wavelets used for the computation of the HWT. Taking into account the drawbacks of the bishrink filter and the sensibility with the selection of the mother wavelets we propose a denoising method in two stages in a multi-wavelet context. Some simulation examples and comparisons prove the performances of the proposed denoising method.
An improved version of the inverse Hyperanalytic Wavelet Transform
The success of wavelet techniques in many fields of signal and image processing was proved to be highly influenced by the properties of the wavelet transform used, mainly the shiftinvariance and the directional selectivity. In the present paper we propose an improved version of the inverse Hyperanalytic Wavelet Transform (HWT), which uses hyperanalytic mother wavelets. We have already proposed implementations of the HWT and of its inverse (IHWT). The implementation supposes the computation of the discrete wavelet transform (DWT) of the hyperanalytic signal associated to the input signal. Our old computation method of the IHWT extracts the real part of the signal at the output of the inverse discrete wavelet transform (IDWT). The aim of this paper is a new implementation of the IHWT, which permits a better shift invariance. We will compare this implementation with our previous one, with the DWT and with Kingsbury's Double-Tree Complex Wavelet Transform (DT CWT).
A Bayesian Approach of Hyperanalytic Denoising
2008
The property of shift-invariance associated with a good directional selectivity are important for the application of a wavelet transform, (WT), in many fields of image processing. Generally, complex wavelet transforms, like for example the Double Tree Complex Wavelet Transform, (DTCWT), poses these good properties. In this paper we propose the use of a new implementation of such a WT, recently introduced, namely the hyperanalytic wavelet transform, (HWT), in denoising applications. The proposed denoising method is very simple, implying three steps: the computation of the forward WT, the filtering in the wavelets domain and the computation of the inverse WT, (IWT). The goal of this paper is the association of a new implementation of the HWT, recently proposed, with a maximum a posteriori (MAP) filter. Some simulation examples and comparisons prove the performances of the proposed denoising method.
IMAGE DENOISING USING DUAL TREE COMPLEX WAVELET TRANSFORM
Image denoising is an important task which finds its application as a task itself and also as a sub task in other processes. Wavelet analyses provide high resolution and are very useful in image processing applications. But there were few factors which delayed the progress of using wavelets. Many researchers have been carried out in this field to extract the advantages of wavelets. This paper presents a survey and simulation of image processing based on DT-CWT. Here, a clearer version of an image is recovered from its noisy observation by the use of Dual Tree Complex Wavelet Transform (DT-CWT) along with Byes thresholding. Convolution based 2D processing is employed for simulation. An improvement in PSNR was observed which clearly tells about the enhancements that can happen in the field of image processing by the use of DT-CWT.
Fluctuation and Noise Letters, 2012
Published 15 Communicated by Stefania Residori 16 Throughout recent years, many wavelet transforms (WTs) were used in digital image 17 processing: the discrete WT (DWT), the stationary WT (SWT) or the hyperanalytic 18 WT (HWT). All these transforms have in common a feature, the mother wavelets (MW). 19 A great number of MWs was already proposed in literature. The purpose of this paper 20 is the selection of MW for hyperanalytic Bayesian image denoising on the basis of its 21 space-frequency localization. The MW with the same space-frequency localization as the 22 elements of the input image gives the better results. Some procedures for the evaluation 23 of the space-frequency localization of MWs and input images are proposed and applied 24 to optimize the results obtained by the simulations of denoising, indicating the most 25 appropriate MW. 26 May 25, 2012 16:6 WSPC/S0219-4775 167-FNL 1250009 A. Isar
IMAGE DENOISING USING DUAL TREE COMPLEX WAVELET
Image denoising is an important task which finds its application as a task itself and also as a sub task in other processes. Wavelet analyses provide high resolution and are very useful in image processing applications. But there were few factors which delayed the progress of using wavelets. Many researchers have been carried out in this field to extract the advantages of wavelets. This paper presents a survey and simulation of image processing based on DT-CWT. Here, a clearer version of an image is recovered from its noisy observation by the use of Dual Tree Complex Wavelet Transform (DT-CWT) along with Byes thresholding. Convolution based 2D processing is employed for simulation. An improvement in PSNR was observed which clearly tells about the enhancements that can happen in the field of image processing by the use of DT-CWT.
A Bayesian approach of wavelet based image denoising in a hyperanalytic multi-wavelet context
WSEAS Transactions on Signal Processing, 2010
We propose the use of a new implementation of the hyperanalytic wavelet transform, (HWT), in association with a Maximum a Posteriori (MAP) filter named bishrink. The denoising methods based on wavelets are sensitive to the selection of the mother wavelets. Taking into account the drawbacks of the bishrink filter and the sensitivity with the selection of the mother wavelets we propose a denoising method in two stages in a multi-wavelet context. It is based on diversification followed by wavelet fusion. Some simulation examples and comparisons prove the performances of the proposed method.