Medical Image DeNoising Schemes Using Different Wavelet Threshold Techniques

In recent years most of researcher’s has done tremendous work in the field of medical image applications such as Magnetic Resonance Imaging (MRI), Ultra Sound, CT scan but still there are many research and experiments in medical imaging field and diagnosing of human health by Health Care Institutes. There is a growing interest for medical imaging denoising as a hot area of research and also imaging equipment as a device. It is used for better image processing and highlighting the important features. These images are affected with random noise during acquisition, analyzing and Transmission process. This results in blurry image visible in low contrast. Wavelet transforms have effective method to separate the noise from the original medical image by using threshold techniques without affecting the important data of an image. Wavelet transform enables us to use the forward wavelet transform to represent subband of the original image in decomposition process then reconstructing this sub band coefficients to original image using inverse wavelet transform. In this work, the quality of medical image has been evaluated using filter assessment parameters like Variance, standard deviation, the squared difference error between original medical image & de-noised image (MSE) and the ratio between original image & noisy image. From numerical results, we can see that the algorithm is efficient de-noising of noisy medical image. When, investigating with Baye’s threshold techniques it achieved the Best value of peak signal to noise ratio (PSNR). For best medical image de-noising, the wavelet based denoising algorithm has been investigated and results of Baye’s techniques and hard & soft threshold methods have been compared. Keywords—Baye’s Wavelet threshold; Discrete Wavelet; Medical Image De-noising; Magnetic Resonance Imaging (MRI)


I. INTRODUCTION
Most of medical diagnostic equipment has applications such as magnetic resonance imaging (MRI), criminal identification systems (CIS), agricultural and biological research (ABR) uses the concept of digital image processing.The term image de-noising is the best tool used in these applications, where it effectively captures the noise from corrupted medical image and preserving with the valuable data and important features of the medical image [1] [2].
The motivation of using Medical Resonance Imaging (MRI) as a hot area because of it's related with human health.
The medical Resonance imaging (MRI) very useful and low cost in diagnosis the human health and mapping the diagnosis output of the medical image in real and refine it as image quality [3] [4].
During image acquisition and transmission, it has been usually observed that random noise always occurs at another end.In previous work, many researchers achieved good results in PSNR but not in MSE or visa-versa.Our work gives Good results in both PSNR and MSE [6] [7].
Most of medical images are vulnerable to noise.This noise causes problems such as a blurred vision of images.Therefore, it is not easy for the medical doctors to examine the abnormalities in human in the invisible image.Most of medical imaging applications have been affected with random noises during Acquisition and transmission process that required improve and recover hidden data and details coefficients from noisy medical image.
Baye's threshold techniques provide good results when compared to Soft and Hard thresholds in terms of MSE and PSNR values as shown in the simulation results.

II. WAVELET TRANSFORM
The main difference between wavelet transform and windowed Fourier transform lies in signal analysis, the wavelet transforms using decomposition process to localize the signal in real time domain and frequency domain.In contrast windowed Fourier analysis has ability to localize the signal in Fourier space domain.Both Fourier and wavelet analysis represent the signal in different version such as sine wave and shifted and scale version which is kind of mother wavelet.But they are similar in windowing scales.The sine wave Fourier transforms have unlimited duration compared with waveform of wavelet transform and the wavelet forward to be irregular waveform.The wavelet Mathematical formula can be written as follows [5].The equation (1) has been expressing a mathematic syntax of Fourier analysis and transform:

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(1) www.ijacsa.thesai.orgWhich mathematically is the sum over all time of the signal f(t) multiplied by Exponential formula.(In mathematic the Exponential formula can be expressed as real and imaginary of sinusoidal vectors).
The Fourier coefficients F (ω) and sinusoid components of original image are results of applying Fourier transform in image processing, when multiplied by sinusoid of frequency.Similarly, the equation (2) expressing mathematic syntax of continuous wavelet transforms which is integration over whole time of the signal multiplied by shift and scale version of the wavelet function.

III. THRESHOLDING
The threshold techniques is an effective and necessary tools in wavelet transform which used to calculate the wavelet coefficients using 1-D or 2-D or 3-D dimensional wavelet array A [i,j] sized with i,j=1 to M that is define the element numbers of array.The Tb is a threshold parameter which remains the wavelet coefficient and wavelet power in thresholding process.The scientists Donoho and Johnstone gave the best choice of threshold in (1994).They showed that the threshold discards the smaller wavelet coefficients and preserve the larger coefficients than threshold level [12] [13].

A. Hard threshold
The hard threshold techniques deal with wavelet coefficients that less than threshold level after computed the wavelet transform and inverse wavelet transform by sitting all the coefficients to zero.Mathematically, the hard threshold formula is represented as follow in equation ( 3).(3)   is computed by the median estimator shown in equation (7).

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The details coefficients and sub band [LH, HL and HH] are generated while using wavelet decomposition process, the signal variance measurement x  estimated by equation ( 8) And σ x is the signal variance without noise defined as the squired max value of differences variance of (noise image and additive white noise image) which compared to zero, performed using standard MATLAB command.

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The standard deviation is defined as the average amount by which individual data from medical image sub band confidents differ from the arithmetic mean of all the data in the set.Lk is the length of the sub band at kth scale.

V. IMAGE DE-NOISING ALGORITHM
The Image De-noising Algorithm is used to extract the noise from during acquisition and transmission and achieve the best image quality in medical image processing, after performed the discrete wavelet transform for original image, and then implementing the bayes wavelet threshold to remove the noise, which affected the visibility of the medical image.And finally the inverse wavelet transform performed to recover the clarity of decomposed medical image.As following steps:

A. Perform the decomposition on the two of original medical images X, Y corrupted by Additive Gaussian Noise using wavelet transform
B. Chose the bayes threshold from equation ( 5) or ( 6) by estimate the measurements a) Estimate the noise variance σ2 using equation ( 7).b) Estimate the additive white noise variance σ y using equation (9).c) Estimate the signal variance σ x using equation (8).

VI. EXPERIMENTS ANALYSIS AND OUTPUTS
The laboratory work implemented on the two of medical images with same size (256×256) named (gland pituitary & Prostate).These images are defined as Xs, r & Ys, r matrix, which taken s, r = 1 to N parameter as image size, and it is a gray scale image.The problems were occurred while transmission and acquisition of original image.The image was affected by noise which could not be diagnosed by doctors and health institutes due to invisibility in image while investigating patient.To overcome on this issue, the forward wavelet transforms, bayes wavelet threshold and inverse wavelet transform techniques are effective tools to separate the noise from original images using wavelet decomposition & reconstructions process.After decomposition, bayes threshold have been applied for wavelet details coefficients and to assess the performance, the de-noising threshold algorithm have to add the variance noise measurement σ 2 = 0.04 of white Gaussian noise to original image for getting high peak signal to noise ratio (PSNR) measurement an d low mean square error (MSE) to assess the quality of reconstructed image compared with wavelet soft and hard threshold that measured by the equation (10) mse PSNR Where the signal to noise ratio measurement is defined as the ratio of signal power to the de noise power of the denoised medical image, often expressed in decibels The mean square error (MSE) of medical image in equation ( 11) is an estimator, which measures the average of the square "errors", that is, the difference error between original medical images (X) and synthesis image (X^).The Experimental work have been carried out by using bayes threshold to estimate the medical image quality using PSNR & MSE measurements with various wavelet threshold methods and various wavelet packages which have been presented in table I, II.From the tables, it can be understand that the lower value of MSE and higher value of PSNR in bayes threshold is vice versa in soft threshold and hard threshold.Which reveals that, bayes threshold in medical image de-noising is effective tool based on the experimental results.The bayes threshold presents the visual quality while compared with soft and hard.Moreover, Bayes threshold has high efficiency and good performance than soft and hard threshold.The MSE ratio of Soft threshold, hard threshold and Bayes threshold of gland pituitary and prostate image have been shown in figure (3&4).While figure (5&6) depicts the PSNR ratio of Soft threshold, hard threshold and Bayes threshold gland pituitary and prostate image.For future work, I suggest using different kinds of images.Like CIS, Agricultural, biological and geographical images for mapping and navigation.

Fig. 1 .
Fig. 1.The decomposition process of DWT at second levelFig.(1) Depicts the decomposition of the signals by using high pass and low pass filters respectively to analyze the low and high frequencies and then measuring the amount of detailed information in the signal by using up sampling and down sampling operation.Both up sampling and down thresholdThe soft threshold work similar to hard threshold discarded all the coefficients less than threshold level to zero.It's also minimizing the magnitude of preserve wavelet coefficients to be equal with largest discarded coefficient.The soft threshold formula is represented as follow in equation (4) DE-NOISING ALGORITHM The Baye's threshold technique has a ability to forming the threshold wavelet sub band coefficients from medical image in Bayesian Frame Work (BFW) during the decomposition process for wavelet coefficients, In Fig.2, De-nosing algorithm model using discreet wavelet transform (DWT) at 2nd-level of decomposition have been proposed.It has been assumed in Generalized Gaussian distribution (GGD) and carefully finds the threshold Tb to reduce the thresholding risk, which affect to the important data in wavelet details and approximation coefficients.Finally, the performance of this thresholding is better for de-noising medical image compared with other threshold techniques[14][16].

Fig. 2 .
Fig. 2. Proposed De-nosing Algorithm Model using discreet wavelet transform (DWT) at 2nd-level of decomposition A. Estimation Parameters for Proposed Algorithm This section defines the adaptive parameters to proposed de-noising algorithm for medical image decomposed sub band coefficients which determine the threshold level (T b ) in equation (5) for different details and approximation sub band coefficients that depend on sub branch equation, which compare the max value of difference variances compared to zero σ y -σ2 ≥ 0, by equation (3).  x b T / 2 

TABLE I .
MSE RESULT OF GLAND PITUITARY & PROSTATE IMAGES TEST WITH VARIENCE 0.04