GRD Journals | Global Research and Development Journal for Engineering | International Conference on Innovations in Engineering and Technology (ICIET) - 2016 | July 2016
e-ISSN: 2455-5703
Medical Image Super Resolution Based On Dual Tree Complex Wavelet Transform 1N.Arivazhaki 2S.Anbhumozhi 1,2
1,2
Department of Electrical and Electronics Engineering KLNCollege of InformationTechnology Sivagangai,TamilNadu, India Abstract
Abstract Most natural images can be approximated using their low-rank components. This fact has been successfully exploited in recent advancements of matrix completion algorithms for image recovery. However, a major limitation of low-rank matrix completion algorithms is that they cannot recover the case where a whole row or column is missing. The missing row or column will be simply filled as an arbitrary combination of other rows or columns with known values. While increasing the size of the image the original image quality will be affected. In order to avoid the loss of quality while enhancing the image, Low rank optimization based on TV and Non Local Means (NLM) Optimized Sparse Method is used. The resulting is then further enhanced with the help of DTCWT. The noises and the pixel differences occurring in the up sampling and down sampling of the images were identified and they were removed based on the proposed method. The resulting images were then further enhanced with the help of DTCWT. In DTCWT DWT, SWT, SVD decomposition was used. Using DTCWT the image size is further increased and also the image is enhanced. This process is more applicable for medical images since the loss in the original pixel information’s were well preserved. The performance of the proposed method is proved using the performance parameters Keyword- DTCWT, NLM, SVD __________________________________________________________________________________________________
I. INTRODUCTION Image processing is a method to perform some operations on an image, in order to get an enhanced image or to extract some useful information from it. It is a type of signal processing in which input is an image and output may be image or characteristics/features associated with that image. Nowadays, image processing is among rapidly growing technologies. Image processing basically includes the following three steps, importing the image via image acquisition tools, Analysing and manipulating the image, Output in which result can be altered image or report that is based on image analysis. The objective of image enhancement is to process a given image so that the result is more suitable than the original image for a specific application. It accentuates or sharpens image features such as edges, boundaries, or contrast to make a graphic display more helpful for display and analysis. The enhancement doesn't increase the inherent information content of the data, but it increases the dynamic range of the chosen features so that they can be detected easily. The greatest difficulty in image enhancement is quantifying the criterion for enhancement and, therefore, a large number of image enhancement techniques are empirical and require interactive procedures to obtain satisfactory results. Image enhancement methods can be based on either spatial or frequency domain techniques.
II. METHOD We first describe how image degradation processes such as blurring and down-sampling effects are modelled. We then describe the solution for the inverse problem of recovering the HR image from the LR image, using low-rank and TV Regularizations. Fig 1 shows that block diagram of proposed work. The proposed method has been evaluated qualitatively through visual inspection and quantitatively by comparing with manual delineation results.
Fig. 1: Block Diagram of Proposed Work
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Medical Image Super Resolution Based On Dual Tree Complex Wavelet Transform (GRDJE / CONFERENCE / ICIET - 2016 / 067)
Blur is added to the input image. Up sampling and down sampling is employed to the blur added image. The noises occurring due to the up sampling and down sampling of the images were then handles based on Low rank optimization process. The noises in the optimized images were then removed using lagrangian operations. The same noises were identified based on optimization using the solution for regression problem. The noises in the optimized images were then removed using Non local means filter. Sparse coding is then applied to the image and then convex minimization problem is then handles and then finally reconstructed High resolution image is obtained. High-resolution (HR) medical images provide rich structural details that are critical for accurate image postprocessing and pathological assessment of bodily organs . However, image resolution is limited by factors such as imaging hardware, signal to noise ratio (SNR), and time constraints. Image SNR is proportional to voxel size and the square root of the number of averages in the voxel. This requires significantly longer scanning time, which may not be practical clinically. A possible alternative approach to this problem is image post-processing. For this, interpolation methods (nearest neighbour, linear, and spine) are generally employed due to their simplicity. However, as pointed out in , interpolation methods generally blur the sharp edges, introduce blocking artifacts in lines, and are unable to recover fine details. In view of this, we take a super-resolution (SR) approach for resolution enhancement of LR images. Interpolation methods are not considered as SR methods since they do not consider the image degradation process (e.g., blurring, and down-sampling). This process is repeated to minimize the energy of the difference. Non-local means (NLM) is a method proposed to take advantage of image self-similarity . Specifically, the input LR image is first demonised and the similar patches are used to reconstruct to a HR image. A correction step is then applied to ensure that the down-sampled HR image is close to the demonised LR image. The reconstruction and correction steps are iterated in a multi-scale manner. In another work, NLM was employed to enhance the resolution of a single LR T2 image with the guidance from an HR T1 image. Input image is decomposed using dual tree complex wavelet transform (DTCWT). By decomposing the image we get low sub band image through low pass filtering and high sub band image through high pass filtering. Due to low pass filtering, high frequency components are lost, which contain information of edges, fine line details etc. So, interpolation is performed on high frequency components. For interpolating the coefficients, lanczos interpolation is used. This type of interpolation is not linear, but it is sinc function type interpolation. Advantage of using the sinc function type interpolation that it varies with the change in the signal information so better reconstruction can be achieved.
III. EXPERIMENTAL RESULT A. Adding blur The acquired image is affected by factors such as motion blur, field in homogeneity, acquisition time, and noise. The observation model could be mathematically formulated as: T=DSX+n (1) where T denotes the observed LR image, D is a down sampling operator, S is a blurring operator, X is the HR image that we want to recover, and n represents the observation noise. B. Low rank and Total variation The rank of a matrix is a measure of non-degenerateness of the matrix, calculated by the maximum number of linearly independent rows or columns in the matrix. The low-rank property implies that some rows or columns in the matrix can be linearly represented by other rows or columns, indicating redundant information in the matrix. Rank(x) = tr (2) Since the rank of a matrix đ?‘‹ is a non-convex function of đ?‘‹, a common approach is to approximate it using the trace norm tr, which leads to a convex optimization problem. Where N is the number of image dimensionality. And tr denotes total rank.Total variation is to remove noise and handle proper edges in images. It is defined as the integral of the absolute gradients of an image đ?‘‡đ?‘‰đ?‘‹=âˆŤâ”‚âˆ‡đ?‘‹â”‚đ?‘‘đ?‘Ľđ?‘‘đ?‘Śđ?‘‘đ?‘§. (3) The proposed LRTV method is formulated as follows, =argminx 2+áľžrankRank(x)+áľžtvTV(x) (4) where the regularization can be separated into low- rank and total variation terms. The rank of a matrix is a measure of non-degenerateness of the matrix, calculated by the maximum number of linearly independent rows or columns in the matrix. The low - rank property implies that some rows or columns in the matrix can be linearly represented by other rows or columns, indicating redundant information in the matrix. Low- rank prior can be used in matrix completion when only a subset of elements is known. C. Constrained optimization We use the alternating direction method of multipliers (ADMM) algorithm to solve the cost function in Eq. (4). ADMM is proven to be efficient for solving optimization problems with multiple non-smooth terms in the cost function [24]. First, we introduce đ?‘ redundant variables {đ?‘€đ?‘–} i=1 to N to simulate X in each dimension i, by requiring that the unfolded đ?‘‹ along the i-th dimension đ?‘‹(i) should be equal to the unfolded đ?‘€(i) along this dimension đ?‘€i(i). The new cost function is as follows:
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Medical Image Super Resolution Based On Dual Tree Complex Wavelet Transform (GRDJE / CONFERENCE / ICIET - 2016 / 067)
Min xi{đ?‘€đ?‘–} i=1 N‖đ??ˇđ?‘†đ?‘‹ − đ?‘‡â€– 2 +áľžrank tr+áľžtvTV(x) subject to∑đ?‘ đ?‘–=1 âˆ? đ?‘– ‖Mi(i)‖x(i) = Mi(i),i=1,‌,N (5) The obtained low resolution images were upsampled based on nearest neighbor interpolation. The low rank and total variation process is the process of identification of the artifacts in the images occurring due to the up sampling of the images.The artifacts in the images were identified and removed based on, arg minx‖đ??ˇđ?‘†đ?‘‹ − đ?‘‡â€– 2+áľžtvTV(x) + ∑đ?‘ (6) đ?‘–=1 đ?œŒ/2 ‖X-Mi(k) + Yi(k)‖2 This eqn can be solved by gradient descent, where the gradient of TV term is obtained from the associated Euler- Lagrange equation [22]. The terms M and Y were updated continuously till the enhanced images were obtained. The updating of the terms M and Y were done till the difference between the cost functions was minimum. The terms M and Y were updated using Yi(k+1) = Yi(k) + (X(k+1)-Mi(k+1)) (8) In the optimization step the artifacts (noises) in the images were identified. The sampled images were divided into 8x8 patches. Optimization problems were then employed in the process. Here is the coefficient vector and is the regularized parameter used for the identification of the noises in the images. Using constrained optimization process the relationship between the original pixel information and the magnification rate can be identified. The optimization problem helps in defining the artifacts in the images. The identified optimized image pixels were then combined to form the patch again. D. DT-CWT (Dual Tree Complex Wavelet Transform In the proposed image RE technique, DT-CWT decomposes a low resolution input image into high frequency and low frequency subbands. Low-frequency subband images are the low resolution of the original image. Therefore instead of using low-frequency subband images of DTCWT decomposition, which contain less information than the original input image, in proposed method using the input image for the interpolation. Hence, the quality of the enhanced image increases by using the input image for interpolation, instead of the low-frequency sub band images. .By applying IDT-CWT, the resulting output image with the enhanced resolution of MR images with preserving the edges. The output images contain sharper edges than the interpolated image obtained by interpolation of the input image directly.
IV. RESULTS AND DISCUSSION The low resolution images were converted into high resolution images based on the structured sparse representation. The images were then up sampled and then down sampled. Optimizations of images were done based on low rank and Total variation. The images were then up sampled and then down sampled. Optimization of images was done based on the identification of the regression problem. The images were then filtered using NLM filter. Finally structured sparse representation is employed for the images to reconstruct the high resolution images. After applying DTCWT algorithm we get a high reconstructed image.
Fig. 2: Input image
Fig. 3: Reconstructed image
Fig. 4: High reconstructed image
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Medical Image Super Resolution Based On Dual Tree Complex Wavelet Transform (GRDJE / CONFERENCE / ICIET - 2016 / 067)
A. Performance Measures The performance of the enhancement process is measured based on the PSNR, SNR and SSIM calculation. The calculated performance metrics indicates that the proposed method is more efficient compared to the existing methods. The PSNR, SNR and SSIM values were calculated as follows, Signal-to-noise ratio (SNR) in decibels (dB)is used to evaluate the quality of reconstruction: đ?‘†đ?‘ đ?‘… = 20 *đ?‘™đ?‘œđ?‘” 10(│ đ?‘“│/│ đ?‘“ − đ?‘”│ ), where f is the original HR image and is the recovered HR image. SSIM is defined as: SSIM (x ,y)= (Âľx2+Âľy2+C1)(Ďƒx2+Ďƒy2+ C2) (2ÂľxÂľy+C1)(2Ďƒxy+C2) Where đ?œ‡x and đ?œ‡y are the mean values respectively in the original HR image f and recovered image y, đ?œŽx2 and đ?œŽy2 are the variances, Ďƒxy is the covariance of two images, đ?‘?1 = (đ?‘˜1đ??ż) 2 and đ?‘?2 = (đ?‘˜2đ??ż) 2 with đ?‘˜1= 0.01 and đ?‘˜2 = 0.03, and L is the Dynamic range of voxel values. SSIM ranges from 0 to 1, and 1 means perfect recovery.
Fig .5: SSIM to Noise Level
Fig. 6: PSNR to Noise level
NN Spline IBP NLM
SNR
SSIM
30.0159 30.4159 30.0159 30.5159
0.7285 0.7325 0.7335 0.7335
TV 31.0159 0.7385 LRTV-SR 31.5159 0.7435 DTCWT 33.0159 0.7585 Table 1: Comparison of Proposed Method with Other Methods
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Medical Image Super Resolution Based On Dual Tree Complex Wavelet Transform (GRDJE / CONFERENCE / ICIET - 2016 / 067)
V. CONCLUSION The enhancement method is proposed here for the purpose of medical image enhancement has considered some transform techniques, also some medical images such as X-Ray, Ultrasound and MRI. But with the ever increasing technology, new methods will be introduced in the market and that may provide better results than this proposed work. So, with the increasing time, new transforms and images will be tested for providing more benefit to various areas of interests. DTCWT decomposes the low resolution input image into high frequency subbands and low frequency subbands. High frequency subbands. DTCWT is nearly shift invariant, more expansive. The analysis of this work is done using MSE and PSNR measuring parameter and the simulation results of proposed method gives better results than the existing methods. In future work, analyze this methodology among more performance measuring parameter except PSNR and MSE.
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