Address for Correspondence 1 Associate Professor, 2 Research Scholar, 3 Professor, Department of Electronics and Communication Engineering

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1 Research Paper ITERATIVE NON LOCAL IMAGE RESTORATION USING INTERPOLATION OF UP AND DOWN SAMPLING 1 R.Jothi Chitra, 2 Sankaran and 3 V.Nagarajan Address for Correspondence 1 Associate Professor, 2 Research Scholar, 3 Professor, Department of Electronics and Communication Engineering Adhiparasakthi Engineering College, Melmaruvathur , Tamil Nadu,, India ABSTRACT This research paper proposes an image restoration technique using interpolation of up and down sampling.image restoration is a function of removing distortion from a noisy image in order to recover the original image. Here, image restoration is performed in three stages. First, a high variance noisy input image is added and denoising is implemented by kernel estimation. In this, the constant noise level is added and iteration is performed. Second, inpainting is carried out using the damaged portion of an image and restoration is done by restoring the local properties of the image. Third, image can be restored by selecting the sampling rate and interpolation of up and down sampling. For each case, the image parameters like PSNR and are evaluated. Performance graph and tabulation are obtained using the above said quality metrics. The better efficiency of proposed iterative image restoration for image denoising and inpainting is achieved when compared to other interpolation techniques. Using this method convergence time is also reduced. KEYWORDS: Sampling, Image Restoration, Interpolation, Inpainting, Sampling rate selection. I. INTRODUCTION Images are created to exhibit useful information. The original image gets degraded due to some disturbances in image acquiring. In the image processing field, image restoration plays asignificantpart in order to acquire quality image from noisy or corrupted image. Denoising is one of image restoration method to eradicate the noise present in the input image. Digital images are often corrupted by different types of noises. Image quality is spoiled by the unnecessary information which is the noise and they are caused by external disorder.image restoration is a function of captivating a noisy image and estimating the original image. The main intention of image restoration is to balance the defects which can corrupt the original input image. Basically, it tries to carry out an action on the image that is the converse of the imperfections in the image formation method. The noise in the image can be reduced by estimating the noisy pixel and the noisy pixel is replaced by predicted values. It is not possible to get useful information directly from the image pattern in some realistic situations. Image restoration algorithm deviates from image enhancement methods and image restoration largely depends on the models for the degrading process. Inpainting and interpolation are image restoration process to achieve quality image. The phrase digital image inpainting was coined by Bertalmio et al. [1].Renovation ofmisplaced or broken portions of images or videos is one of the common practices in image restoration. Inpaintingis also called as retouching and there are abundant applications for restoring the damaged painting and photographs by replacing the selected things [2]-[8]. The main objective is to renovate the mislaid or scratched portions of an image such that it is possible to attain a clearer image and its uniqueness is achieved. It also removes the unwanted things and writings on the image and it can be done by first marking the region in the image that has to be inpainted. Selection of region in the image purely depends on the user requirements. Interpolation is the method of shaping the values of a function at positions that is lying between the samples.interpolation is an approach through which images are enlarged. It is done by placing a continuous function through the discrete input samples. The input values of the arbitrary positions are first evaluated. An infinite bandwidth signal is generated during sampling that is band limited. The inverse operation is followed in interpolation that is bandwidth is limited so that it can be applied to discrete signal in the low pass filter. The signal lost in the sampling process is reconstructed by smoothing the data samples within the function. Interpolation is one of the basic operations in the image processing field. The quality of the image is greatly depends on the used interpolation technique. Deterministic and Statistical interpolation are the two categories in the interpolation techniques. In case of deterministic interpolation, certain variable is assumed between the sample points. It is equivalent to linear interpolation. The estimated error is minimized by approximating the signal in case of statistical interpolation. Due to this approximation, original sample values are obtained without any replication. Statistical methods are computationally inefficient. The rest of the paper is organized as follows. Section II describes the related work. Proposed method is explained in section III.Section IV presents the experimental results. In section V includes conclusion. II. RELATED WORK NONLOCAL IMAGE RESTORATION Different non local image restoration techniques have been employed till now but they still do not produce optima[9].contrary to intensity images, each pixel of a range image expresses the distance between a known reference frame and a visible point in the scene. Range images are acquired by range sensors that, when acquired at video rate, are either very expensive or very limited in terms of resolution. The following are the number of methods for restoring the images. The goal of sparse coding [10] is to represent input vectors approximately as a weighted linear combination of a small number of (unknown) basis vectors. These basis vectors thus capture high-level patterns in the input data. In order to apply singular value decomposition (SVD) from a bilateral variance

2 estimation perspective here simultaneous sparse coding. Sparse coding is a method for discovering good basis vectors automatically using only unlabeled data [11]. The standard generative model assumes that the reconstruction error is distributed as a zero-mean Gaussian distribution with covariance σ 2 I. As an improvement over the original version, the basis images from the new transform are sharply localized in their smoothness exhibit and frequency domain along their main ridges in the spatial domain. In practice, this improved regularity of basis images helps reduce the artifacts in processed images; consequently making the new method is more favourable choice for various image processing applications. Block matching is realized by grouping and filtering is performed by dwindling in a 3-D transform domain. Image fragments used are square blocks with fixed size. The measures established out in this technique are Similar blocks are grouped and then matched block are stacked together to form a 3- D array.the parameters PSNR and are obtained, but it is less efficient compared to other filtering techniques. CSR is to treat the local and non-local sparsity constraints as peers and then incorporate them into a unified variational framework. It is worn to distinguish the significance of organizational ambiguity of causal image signal. CSR affords capable performance compared to BM3-D since PSNR of CSR is least similar and it is higher to other competing schemes[13]. In CSR, sparsity coefficients are not randomly distributed. It is extremely different from both SVD and BM3-D on the image which has a regular texture pattern. The bilateral estimation is based on the condition when the neighborhood window is autonomous of the coefficients which are outside the window. But it largely depends upon the signal behavior and its property. In this technique, sigma value is made constant and noise level is increased. If the noise level increases PSNR value decreases. It needs two parameters that are specified by the user: size of the patch and the number of the patches that are similar. Compared to other filtering techniques SAIST achieves more significant when the noise level increases. The visual image quality is more realistic in case of SAIST [13]. Classical image denoising algorithms is not applicable to image inpainting. In ordinary image enhancement applications, the pixels contain information about the real data and the noise, while in image inpainting; there is no significant information in the region to be inpainted. Bertalmio et al [2] has introduced a digital inpainting for still images that are used to obtain better results. For relatively small areas this algorithm requires some minutes in order to perform the image inpainting. It is mainly used for restoring the photographs, scratched images and for removing text in the photos. The area to be inpaintedconsists of information surrounded in that region and then problem is formulated. Inpainting performs three functions. First one is restoration of films, the second one is texture analysis and the last one is disocclusion. To interpolate losses in films from nearby frames Kokaram et al. [3] use motion estimation and autoregressive models. It is done by copying the right pixel into the gap from neighboring frames. It cannot be implemented to still images or to films where the regions to be inpainted duration many frames. To estimate the variation in color, smoothness 2-D Laplacian is used. The variation is propagated along the isophote direction [2]. In order to smooth the inpainted region, this algorithm runs a few diffusion iterations and it occurs after every few step in inpainting process. There are number interpolation techniques that have been developed and are found in the literature. The most important methods used are the nearest neighbor, linear and spline interpolation techniques. Least commonly used are the polynomial and Lagrange interpolation methods. The accuracy and computational cost of interpolation algorithm are openly attached to the interpolation kernels which are the goal of design and examinations. It consists of 1-D and 2-D case and 2- D is an extension of the 1-D case. III. PROPOSED WORK Image restoration can be implemented in three cases. First, is high variance noise is added to the input image and the noise is reduced by iteration method. Second, is that the damaged part of the image is selected and image inpainting is performed. Third, is that image restoration in done by interpolation of up and down sampling. A. Denoising Any size of the image can be taken as input image. In this high variance noise is added to the input image. Noisy image is denoised and the quality metric like PSNR and is calculated for noisy image and resulted denoiseimage.denoising is done by iterative method. B. Inpainting In this the damaged image is selected and after inpainting is performed the clear image can be attained. For this PSNR and are calculated. In automatic digital inpainting,. = 0 (1) Evolutionary form = L. N (2) where L is smoothness estimator and N is isophotedirection.inpainting can be used for text removal, photo restoration, special effects, and scratch removal. The spatial frequency content can be restored by sampling theorem if the images contain textures with spatial discontinuities. Simpler models are used to approximate the results when the regions are smaller. The general expression is expressed as (, ) = (, )+ (, ), (, ) (3) Where n is inpainting time,(x,y) are pixel coordinates and is the rate of improvement. (, )is updated image. (, )is improvement version of updated image.

3 Fig 1. Block diagram of proposed method C. Interpolation From the input image, interpolation is done by selecting the sampling rate in order to convert digital into continuous signal. It is mainly useful for resolution enhancement, error concealment etc. The linear interpolation can be expressed as ( ) = ( ) = ( 1, 2,.. ) (4) where an interpolated value g(n) at some coordinate n in a space of dimension q is expressed as a linear combination of the samples g k evaluated at integer coordinates n=(ni,n2..nq), the weights being given by the values of the function ( ).Typical values of the space dimension correspond to gray images (2D), with q = 2, and color image (3D), with q = 3. IV. EXPERIMENTAL RESULT In this section, the experimental results are shown. The PSNR and are calculated and they are plotted in the graph for different noise levels. The Structural SIMilarity () index is a method for measuring the similarity between two images.psnr is used to measure image quality retention in db. The general expression for PSNR is = 10 (5) MSE can be expressed as MSE =,[f(i,j) g(i,j)] (6) TABLE I : For Lena Image PSNR & Value For 4 Different Noise Levels LEVEL PSNR OF NOISY IMAGE PSNR AFTER ITERATION Table 1.shows the PSNR and values for the lena at various noise intervals. Fig 2 and Fig 3 shows the PSNR graph and graph. TABLE II: For Monarch Image ThePsnr&Ssim Value For Different Methods ( LEVEL 30) METHODS PSNR VALUE VALUE BM3D LSSC CRC SAIST Proposed method (Iteration) PSNR noise level (%) Fig 2. PSNR graph forlena image for 4 different noise level PSNR analysis analysis proposed image restoration proposed image restoration noise level (%) Fig 3. graph forlena image for 4 different noise level TABLE III: For Lena Image (example)thepsnr Values For Different Noise Density With Other Filters DENSITY 10 DENSITY 15 DENSITY 20 DENSITY 30 PSNR value for noisy image BM3D CRC LSSC SAIST PROPOSED METHOD (ITERATION)

4 Fig4 :Output of the proposed method a) noise level 5 b)noise level 10 c) noise level 15 d) noise level 40 e) denoised image Fig 5 : a)damaged images b) inpainted images V. CONCLUSION Adding noise with high variance and by removing a large part of the input image with random selection of region (in both edges& flat region).denoising is done by using kernel estimation method. Restoration of Fig 6:a)Downsampled image b) upsampled image lost data from the damaged image by estimating the local property of patches.the efficiency of the proposed restoration scheme will be compared with conventional methods. PSNR and values are calculated and the performance graphs are plotted.

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