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\title{MRI Denoising Using Waveatom Shrinkage By Geetika Dua \& Varun Raj}
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             \author[1]{Dr. Geetika  Dua}

             \author[2]{Varun  Raj}

             \affil[1]{  GGSIPU Delhi}

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\date{\small \em Received: 4 February 2012 Accepted: 29 February 2012 Published: 15 March 2012}

\maketitle


\begin{abstract}
        


It is well known that noise in Magnetic Resonance Image has a Rician distribution.Unlike additive Gaussian noise, Rician noise is signal dependent, and separating signal from noise is a difficult task. In this paper, a denoising technique is used in order to remove Rician noise from MRI using Waveatom shrinkage. De-noising by any shrinkage technique is highly sensitive to the threshold selection. Here to estimate the noise variance, histogram based technique is used and to calculate the shrinkage threshold a new technique is proposed. This method is applied to both simulated images and real images. Wave atom transform has been applied for different noise levels. This has been done in order to find more accurate results. A comparative analysis of wave atom and wavelet is also performed.

\end{abstract}


\keywords{De-noising, Histogram, Magnetic Resonance Image, Rician Noise, Variance Estimation, WaveAtomTransform.}

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\let\tabcellsep& 	 	 		 
\section[{INTRODUCTION}]{INTRODUCTION}\par
agnetic resonance imaging (MRI) is a medical imaging technique that measures the response of atomic nuclei of body tissues to high frequency radio waves when placed in a strong magnetic field and that produces images of the internal organs. Magnetic Resonance Imaging has proven to be particularly valuable for examination of the soft tissues in the body and is a commonly used form of medical imaging. Because of the resolution of MRI and the technology being essentially harmless it has emerged as the most accurate and desirable imaging technology. It was shown that pure noise in MR magnitude images could be modeled as a Rayleigh distribution. Afterwards, the Rician model was proposed as a more general model of noise in MR images. Sources of MR noise include thermal noise, inductive losses, sample resolution, and field-of-view. Despite significant improvements in recent years, magnetic resonance images often suffer from low SNR especially in cardiac and brain imaging. Therefore, noise reduction techniques are of great interest in MR imaging. 
\section[{II.}]{II.} 
\section[{RELATED WORK}]{RELATED WORK}\par
The image processing literature presents a variety of de-noising methods. Many of the popular de-noising algorithms suggested are based on wavelet thresholding \hyperref[b0]{[1]}- \hyperref[b4]{[4]}. These approaches attempt to separate significant features from noise in the frequency domain and simultaneously preserve them while removing noise. If the wavelet transform is applied on MR magnitude data directly, both the wavelet and the scaling coefficients of a noisy MRI image become biased estimates of their noise-free counterparts. Therefore, it was suggested \hyperref[b2]{[2]} that the application of the wavelet transform on squared MR magnitude image data would result in the wavelet coefficients no longer being biased estimates of their noise-free counterparts. Although the bias still remains in the scaling coefficients, it is not signal-dependent and can therefore be easily removed. The difficulty with wavelet or anisotropic diffusion algorithms is again the risk of over smoothing fine details particularly in low SNR images \hyperref[b5]{[5]}. From these points, it is understood that all the algorithms have the drawback of over-smoothing fine details. In \hyperref[b6]{[6]}, stated that oscillatory functions or oriented textures have a significantly sparser expansion in wave atoms than in other fixed standard representations like Gabor filters, wavelets and curvelets. In \hyperref[b7]{[7]}, denoising using Wave Atom is done by estimating the noise variance by trial and error method. In [8], denoising using Wave Atom is done by estimating the noise variance by histogram technique. 
\section[{III.}]{III.} 
\section[{RICIAN NOISE}]{RICIAN NOISE}\par
Magnetic resonance magnitude image data are usually modelled by the Rician distribution  {\ref [9]}. The magnetic resonance signals are acquired in quadrature channels. Each signal produces an image that is degraded by a zero-mean Gaussian noise of standard deviation as 0. The two images are then combined into a magnitude image and the Gaussian noise PDF is transformed into a Rician noise PDF. The joint probability density of the noise from two quadrature channels can be expressed as [10]:2 0 2 2 2 0 2 exp 2 1 , i r i r n n n n p (1)\par
The expectation values for the mean magnitude and the variance are \hyperref[b2]{[2]}:4 exp 2 I 2 0 2 0 X 2 0 4 2 1 2 0 2 2 2 0 4 2 0 2 0 2 2 1 X I X X I X (2) M Global Journal of Researches in Engineering Volume XII Issue v v v v IV Version I 23 ( D D D D ) F © 2012 Global Journals Inc. (US) 2 0 2 2 exp 2 2 0 2 0 2 2 2 X X I 2012 March Geetika Dua \& Varun Raj Author :ECE Deptt., GGSIPU Delhi. E-mail : geetikadua09@gmail.com 2 2 0 4 2 1 2 0 2 2 2 0 4 2 0 2 0 2 2 1 X I X X I X (3)\par
where 0 I and 1 I are modified Bessel functions of the first kind and X denotes the MR magnitude image.\par
IV. 
\section[{WAVEATOM TRANSFORM}]{WAVEATOM TRANSFORM}\par
Wavelet transform is a well known multiresolution analysis tool capable of conveying accurate temporal and spatial information. Wavelets better represent objects with point singularities in 1D and 2D space but fail to deal with singularities along curves in 2D. Therefore wavelet representation does not offer sufficient sparseness for image analysis. Following the introduction of wavelet transform, research community has witnessed intense efforts for development of wave atoms, ridgelets \hyperref[b10]{[11]}, contourlets \hyperref[b11]{[12]} and curvelets \hyperref[b12]{[13]}. These tools have better directional and decomposition capabilities than wavelets. Wave atoms have a sharp frequency localization that cannot be achieved using a filter bank based on wavelet packets and offer a significantly sparser expansion for oscillatory functions \hyperref[b13]{[14]}. Wave atoms capture coherence of pattern across and along oscillations whereas curvelets capture coherence only along oscillations. To make our discussion concrete, we need to classify various wave-packet transforms as phase-space tilings. Since a complete collection must span all positions and frequencies, we see that wave packets are actually tiles in phase-space. We say a tiling is universal if it treats democratically all positions and orientations as shown in Figure \hyperref[fig_0]{1}. Two parameters should suffice to index a lot of known wave packet architectures: to index whether the decomposition is multiscale ( = 1) or not ( = 0); and to indicate whether basis elements are localized and poorly directional ( = 1) or, on the contrary, extended and fully directional ( = 0). Wave Atoms corresponds to = =1/2, having an aspect ratio \textasciitilde 2-j/2 ×2 -j/2 in space, with oscillations of wavelength\textasciitilde 2 -j in the codirection .\par
Wave atoms are a variant of 2D wavelet packets which obey the parabolic scaling law: wavelength\textasciitilde (diameter) 2 .\par
V. 
\section[{EXPERIMENTS AND RESULTS}]{EXPERIMENTS AND RESULTS}\par
This section gives a detailed analysis of the proposed MRI de-noising algorithm. It compares and validates the performance of the proposed method using simulated and Real MR images and also compares the performance of the proposed method with Wavelet shrinkage.\par
Determination of threshold is very critical in this work. Input elements with absolute value greater than the set threshold value, are set to 1. In this work a new threshold is proposed which is better as compared to old threshold \hyperref[b14]{[15]}.\par
Old Threshold is given as: val val min max ln \par
After applying threshold criterion inverse Wave Atom transform and inverse Wavelet transform is applied separately and performance of both is compared using four comparison parameters.\par
Four comparison parameters mean square error (MSE), peak signal to noise ratio (PSNR), signal to mean square error (S/MSE) and signal to noise ration(SNR) are used which are defined as: Mean square error (MSE) is given asm i n j j i DN j i N n m MSE 1 1 2 , , * 1 (7)\par
Where m is number of rows in the image, N(i, j) is the noisy image and DN(i, j) is the de-noised image.         
\section[{Peak Signal to Noise ratio (PSNR) is given as}]{Peak Signal to Noise ratio (PSNR) is given as} 
\section[{FUTURE SCOPE}]{FUTURE SCOPE}\par
The field of image processing has been growing at a very fast pace. The day to day emerging technology requires more and more revolution and evolution in the image processing field. The work proposed in this paper also portrays a small contribution in this regard. This work can be further enhanced to de-noise the other type of images, like CT, Ultrasound, X ray images. It will provide a good add on to the already existing denoising techniques. Moreover, for future work we can train our algorithm using various techniques like fuzzy logic or neural network, in order to attain the best output without performing calculations for each and every combination.  
\section[{Global Journal of Researches in Engineering}]{Global Journal of Researches in Engineering}\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-5.png}
\caption{\label{fig_3}(}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-6.png}
\caption{\label{fig_4}Figure. 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-7.png}
\caption{\label{fig_5}Figure. 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-8.png}
\caption{\label{fig_6}Volume}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{March1} \par 
\begin{longtable}{P{0.19568345323741007\textwidth}P{0.12994604316546762\textwidth}P{0.12688848920863308\textwidth}P{0.12994604316546762\textwidth}P{0.12535971223021583\textwidth}P{0.14217625899280575\textwidth}}
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 25\\
Parameters\tabcellsep Denoised using Wave Atom with old threshold\tabcellsep Denoised using Wavelet with old threshold\tabcellsep Denoised using Wave Atom with new threshold\tabcellsep Denoised using Wavelet with new threshold\tabcellsep v v v IV Version I Volume XII Issue v D D D D )\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep (\\
MSE(mean square error) PSNR( peak signal to noise ratio) S/MSE(signal to mean square error) SNR(signal to noise ratio)\tabcellsep 0.0034172 24.6632 dB 17.0783 dB 12.4240 dB\tabcellsep 0.0036304 24.4005 dB 16.8156 dB 12.0257 dB\tabcellsep 0.0022945 26.3931 dB 18.8082 dB 15.2194 dB\tabcellsep 0.002433 26.1386 dB 18.5537 dB 14.6561 dB\tabcellsep Global Journal of Researches in Engineering\end{longtable} \par
  {\small\itshape [Note: F © 2012 Global Journals Inc. (US)]} 
\caption{\label{tab_0}2012 March Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.2376957494407159\textwidth}P{0.15402684563758387\textwidth}P{0.15212527964205816\textwidth}P{0.15402684563758387\textwidth}P{0.15212527964205816\textwidth}}
\tabcellsep Denoised using\tabcellsep Denoised using\tabcellsep Denoised using\tabcellsep Denoised using\\
Parameters\tabcellsep WaveAtom with old\tabcellsep Wavelet with old\tabcellsep WaveAtom with\tabcellsep Wavelet with\\
\tabcellsep threshold\tabcellsep threshold\tabcellsep new threshold\tabcellsep new threshold\\
MSE(mean square error)\tabcellsep 3.5587e-005\tabcellsep 3.8718e-005\tabcellsep 3.3665e-005\tabcellsep 3.5996e-005\\
PSNR( peak signal to noise ratio)\tabcellsep 44.4871 dB\tabcellsep 44.1208 dB\tabcellsep 44.7282 dB\tabcellsep 44.4375 dB\\
S/MSE(signal to mean square error)\tabcellsep 36.9022 dB\tabcellsep 36.5359 dB\tabcellsep 37.1433 dB\tabcellsep 36.8526 dB\\
SNR(signal to noise ratio)\tabcellsep 30.6408 dB\tabcellsep 30.1310 dB\tabcellsep 30.7152 dB\tabcellsep 30.1635 dB\end{longtable} \par
  {\small\itshape [Note: FOR REAL IMAGES: The real images were down loaded from the Open Acess Series of imaging Studies (OASIS) database[17].]} 
\caption{\label{tab_1}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.23589449541284402\textwidth}P{0.1559633027522936\textwidth}P{0.15011467889908256\textwidth}P{0.1559633027522936\textwidth}P{0.15206422018348625\textwidth}}
\tabcellsep Denoised using\tabcellsep Denoised using\tabcellsep Denoised using\tabcellsep Denoised using\\
Parameters\tabcellsep Wave Atom with\tabcellsep Wavelet with old\tabcellsep Wave Atom with\tabcellsep Wavelet with\\
\tabcellsep old threshold\tabcellsep threshold\tabcellsep new threshold\tabcellsep new threshold\\
MSE(mean square error)\tabcellsep 0.0027496\tabcellsep 0.0028503\tabcellsep 0.0019821\tabcellsep 0.0021131\\
PSNR( peak\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
signal to noise\tabcellsep 25.6072 dB\tabcellsep 25.451 dB\tabcellsep 27.0287 dB\tabcellsep 26.7508 dB\\
ratio)\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
S/MSE(signal to\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
mean square\tabcellsep 14.3304 dB\tabcellsep 14.1742 dB\tabcellsep 15.7519 dB\tabcellsep 15.4739 dB\\
error)\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
SNR(signal to noise ratio)\tabcellsep 10.2556 dB\tabcellsep 10.0420 dB\tabcellsep 12.2912 dB\tabcellsep 11.8558 dB\end{longtable} \par
  {\small\itshape [Note: F © 2012 Global Journals Inc. (US)]} 
\caption{\label{tab_2}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.24425287356321837\textwidth}P{0.15241379310344827\textwidth}P{0.15045977011494255\textwidth}P{0.15241379310344827\textwidth}P{0.15045977011494255\textwidth}}
\tabcellsep Denoised using\tabcellsep Denoised using\tabcellsep Denoised using\tabcellsep Denoised using\\
Parameters\tabcellsep WaveAtom with\tabcellsep Wavelet with old\tabcellsep WaveAtom with\tabcellsep Wavelet with\\
\tabcellsep old threshold\tabcellsep threshold\tabcellsep new threshold\tabcellsep new threshold\\
MSE(mean square error)\tabcellsep 0.0071381\tabcellsep 0.0073061\tabcellsep 0.0055929\tabcellsep 0.0058536\\
PSNR( peak signal to noise ratio)\tabcellsep 21.4642 dB\tabcellsep 21.3631 dB\tabcellsep 22.5236 dB\tabcellsep 22.3258 dB\\
S/MSE(signal to mean square error)\tabcellsep 10.1873 dB\tabcellsep 10.0863 dB\tabcellsep 11.2468 dB\tabcellsep 11.0489 dB\\
SNR(signal to noise ratio)\tabcellsep 6.3210 dB\tabcellsep 6.1699 dB\tabcellsep 7.8936 dB\tabcellsep 7.5525 dB\end{longtable} \par
 
\caption{\label{tab_3}Table 4 :}\end{figure}
 			\footnote{© 2012 Global Journals Inc. (US)} 		 		\backmatter  			  				\begin{bibitemlist}{1}
\bibitem[Weaver et al.]{b0}\label{b0} 	 		\textit{},  		 			J B Weaver 		,  		 			Y Xu 		,  		 			D M HealyJr 		,  		 			L 		.  		 	 
\bibitem[Pizurica et al. ()]{b4}\label{b4} 	 		‘A review of wavelet denoising in MRI and ultrasound brain imaging’.  		 			A Pizurica 		,  		 			A M Wink 		,  		 			E Vansteenkiste 		,  		 			W Philips 		,  		 			J B T M Roerdink 		.  	 	 		\textit{Current Med Imag Rev}  		2006. 2  (2)  p. .  	 
\bibitem[Sijbers et al. (2007)]{b8}\label{b8} 	 		‘Automatic estimation of the noise variance from the histogram of a magnetic resonance image’.  		 			J Sijbers 		,  		 			D H J Poot 		,  		 			A J Dekker 		,  		 			W Pintjens 		.  	 	 		\textit{Physics in Medicine and Biology}  		February 2007. 52  (5)  p. .  	 
\bibitem[Candes and Donoho ()]{b10}\label{b10} 	 		‘Curvelets -a surprisingly effective non adaptive representation for objects with edges’.  		 			E J Candes 		,  		 			D L Donoho 		.  	 	 		\textit{Curves and Surfaces},  				 			C Rabut,  			A Cohen,  			L L Schumaker 		 (ed.)  		 (Nashville, TN)  		2000. Vanderbilt University Press. p. .  	 
\bibitem[Wink and Roerdink ()]{b3}\label{b3} 	 		‘Denoising functional MR images: A comparison of wavelet denoising and Gaussian smoothing’.  		 			M Wink 		,  		 			J B T M Roerdink 		.  	 	 		\textit{IEEE Trans Image Process}  		2004. 23  (3)  p. .  	 
\bibitem[Lendl et al. ()]{b15}\label{b15} 	 		‘Estimation of noise image variance’.  		 			M Lendl 		,  		 			K Rank 		,  		 			Unbehauen 		.  	 	 		\textit{IEEE Transaction on Vision,Image and signal processing}  		1999. 146  (2)  p. .  	 
\bibitem[Cromwell ()]{b1}\label{b1} 	 		‘Filtering noise from images with wavelet transforms’.  		 			Cromwell 		.  	 	 		\textit{Magn Reson Med}  		1991. 21  (2)  p. .  	 
\bibitem[Cottet and Germain ()]{b9}\label{b9} 	 		‘Image processing through reaction combined with non-linear diffusion’.  		 			G Cottet 		,  		 			L Germain 		.  	 	 		\textit{MatComput}  		1993. 61 p. .  	 	 (References Références Referencias 10) 
\bibitem[Tinku Acharya et al. ()]{b11}\label{b11} 	 		\textit{IMAGE PROCESSING-Principles and Applications},  		 			Tinku Acharya 		,  		 			. K Ajoy 		,  		 			; John Wiley \& Ray 		,  		 			M C Sons 		.  		2005. Hoboken, New Jersey, A.  	 	 (Publication) 
\bibitem[Tisdall and Atkins ()]{b5}\label{b5} 	 		‘MRI denoising via phase error estimation’.  		 			D Tisdall 		,  		 			M S Atkins 		.  	 	 		\textit{Proc SPIE Med Imag}  		2005. p. .  	 
\bibitem[Rajeesh et al. (2010)]{b7}\label{b7} 	 		‘Noise Reduction in Magnetic Resonance Images using Wave Atom Shrinkage’.  		 			J Rajeesh 		,  		 			R S Moni 		,  		 			S Kumar 		,  		 			T Gopalakrishnan 		.  	 	 		\textit{International Journal of Image Processing}  		March/April 2010. 4  (2)  p. .  	 
\bibitem[Plonka and Ma ()]{b6}\label{b6} 	 		‘Nonlinear Regularised Reaction-Diffusion Filter for Denoising images with Textures’.  		 			Gerlind Plonka 		,  		 			Jianwei Ma 		.  	 	 		\textit{IEEE Trans. Image Processing}  		2008. 17  (8)  p. .  	 
\bibitem[Rajeesh et al. (2010)]{b14}\label{b14} 	 		\textit{Rician Noise Removal on MRI Using Wave Atom Transform with Histogram Based Noise Variance Estimation},  		 			R S Rajeesh 		,  		 			S Moni 		,  		 			T Kumar 		,  		 			Gopalakrishnan 		.  		December 2010. IEEE Communication Control and Computing Technologies. p. .  	 
\bibitem[Antoine and Murenzi ()]{b12}\label{b12} 	 		‘Two-dimensional directional wavelets and the scale-angle representation’.  		 			J P Antoine 		,  		 			R Murenzi 		.  	 	 		\textit{Sig. Process}  		1996. 52 p. .  	 
\bibitem[Demanet and Ying ()]{b13}\label{b13} 	 		‘Wave atoms and sparsity of oscillatory patterns’.  		 			L Demanet 		,  		 			L Ying 		.  	 	 		\textit{Appl Comput Harmon Anal}  		2007. 23  (3)  p. .  	 
\bibitem[Nowak ()]{b2}\label{b2} 	 		‘Wavelet-based Rician noise removal for magnetic resonance imaging’.  		 			R D Nowak 		.  	 	 		\textit{IEEE Trans Image Process}  		1999. 8  (10)  p. .  	 
\end{bibitemlist}
 			 		 	 
\end{document}
