IMAGE NOISE REDUCTION NSCT transform

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order to evaluate the algorithm effectiveness, we use subjective and objective evaluation of the combination evaluation method, objective evaluation method to evaluate the use of peak signal to noise ratio de-noising effect. Experimental results show that, compared to other methods, PSNR is improved, visual effect is improved.
Keywords: image denoising; nonsubsampled Contourlet transform; PSNR HM000073
3.3 Image Denoising Method NSCT transform
3.3.1 NSCT denoising threshold
energy of the transformed NSCT concentrated on a limited transform domain coefficients , most of the remaining smaller magnitude transform domain coefficients. After the transformed Gaussian white noise is still white noise, all the energy distribution in the transform domain coefficients [14]. Since the signal energy is concentrated on a small number of transform coefficients, threshold denoising algorithm is divided into soft and hard threshold threshold method. Redundancy NSCT transform denoising experiments we used hard threshold, the test is better than the soft thresholding. The coefficient NSCT individually with a threshold value set in advance, and if the magnitude of the coefficient is greater than a threshold, is retained; if less than the threshold, then set to zero. Hard threshold NSCT domain:
       (3.8)
where c (m, n) threshold value before treatment NSCT coefficient, the c '(m, n) hard thresholding new NSCT coefficient, T (m, n) is selected as the threshold coefficient. Select K-sigma threshold as the threshold value coefficient,
                                    (3.9)
[sigma] is the noise variance NSCT domain, because the non-orthogonality NSCT transform, so the noise variance directional subband is not equal, so here using Monte Carlo methods to estimate [sigma] [13].
In general, for the high frequency coefficients, since the K-sigma threshold value K is set for Curvelet transform. K is the method of selecting the smallest dimension of the layer so that K = 4, in order to rest on the scale K = 3, for the low frequency coefficients are not disposed of.
However, this paper is NSCT, the experiment results show that a number of references, NSCT better than Curvelet transform frequency selectivity, so this is not a good method of selecting K directly applied, should be properly improved. Edge information and image details are important for an image. In the denoising process, if the threshold selected too large, the transform coefficients will lose some relatively small edge or details.
K value is finally determined by experiment, the threshold value of the coefficient K for the corresponding modification. For the high frequency coefficients, the finest scale layer so K = 3.4, while in other levels so that K = 2.78, the low-frequency coefficients of the same process is not [15].
NSCT coefficient magnitude greater than those of the signal amplitude and energy spread of less noise NSCT coefficient values. Since conversion can NSCT signal energy is concentrated in a few coefficients NSCT, Gaussian white noise on any orthogonal transform base of white noise is still obtained. Select a reasonable threshold for NSCT coefficient thresholding is very important.
NSCT coefficient there is some correlation between the energy of the image transform coefficients NSCT concentration of edges, the amplitude is large, the absolute values of the coefficients of the edge region and larger; noise energy is dispersed, small amplitude region coefficient absolute value sum is small. Because of this feature NSCT coefficients [16,17], in the through each sub band images out NSCT edge region is reduced to retain more threshold coefficient, noise increase threshold value to remove regions more noise, ultimately the effect of image noise removal.
Generally, less energy is dispersed and the noise factor, the image factor and can concentrate a large amount. Definition of a (m, n), where S is the number of B NSCT coefficient, B is the NSCT subband coefficients c (m, n) in the neighborhood. In this paper we take a window size of 3 × 3. It is obtained from the sub-band coefficients of the averaging filter by:
     (3.10)
in the threshold processing, the neighborhood information NSCT binding coefficients, and the amplitude coefficient according to a single neighbor coefficient amplitude size, further improving the PSNR of denoised image.
In the above-described process as the subband processing units, if the central point when the neighbor window edge sub-band, it will exceed the neighboring coefficient subband boundaries, time beyond the boundary of neighboring coefficient subband inner distance coefficients (coefficients exceeding the boundary neighborhood) nearest coefficient (coefficient edge) instead.
In this paper, in conjunction with the threshold neighborhood information is represented as [18]
 (3.11
initial threshold value where T (m, n) of each sub-3.3.1 (3.9) obtained band, min1 entire sub-band a (m, n) the minimum value, the mean Mean1 the entire sub-band a (m, n), and [lambda] is greater than a constant value of less than 2, chapter take λ = 1.06. in this way we can more accurately at the same scale statistics analysis factor at the same level to get through all the analysis and partial range of more precise image information thus effectively retaining the useful information we need, reduces noise View full please + Q:.. 351 916 072 Gets
Abstract I
ABSTRACT II
Chapter 1 introduction 1
1.1 background 1
Research Status 1.2 2
1.2.1 Overview 2 denoising
study of history 2 1.2.2 multiscale geometric analysis of
the development of multi-scale geometric analysis 1.2.3 3
main work of this paper and 1.3 section 5 arrangements
theory Chapter 2 multi-scale geometric transformations 6
2.1 6 wavelet transform
Contourlet transform 2.2 6
2.2 8 Laplacian pyramid
2.2.2 filter direction (the DFB). 9
2.2.3 column direction of the filter pack 12
2.3 15 nonsubsampled Contourlet transform
2.3.1 Sampling non Laplace 15 pyramid decomposition
2.3.2 nonsubsampled directional filter set 16
2.3.3 nonsubsampled Contourlet transform 17
2.4 18 Summary
Study 19 image denoising method based on NSCT transform Chapter 3
3.1 Introduction 19
3.2 19 the method of thresholding
3.2 .1 conventional threshold selection method 19
3.2.2 common threshold selection method 21 function
3.2.3 quality evaluation standard for image denoising 22
3.3 22 Study image denoising method based on NSCT transform
3.3.1 NSCT denoising threshold 22
3.3.2 chapter 25 algorithm process described
3.3.3 nonsubsampled Contourlet transform image denoising method flowchart 26 is
26 is 3.4 Summary
Chapter 4 simulation results and analysis 27
4.1 plus noise noise Reduction and analysis results 27
FIG original 4.2 denoising noisy results and analysis 29
4.3 31 Summary
Chapter 5 Summary and Outlook 32
5.1 32 herein summary
5.2 Outlook 33
Acknowledgments 33
References 35
Appendix 37
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