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\title{An Optimal Factor Analysis Approach to Improve the Waveletbased Image Resolution Enhancement Techniques}
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             \author[1]{Yitian  Zhao}

             \affil[1]{  Cranfield University}

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\date{\small \em Received: 10 December 2015 Accepted: 3 January 2016 Published: 15 January 2016}

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\begin{abstract}
        


The existing wavelet-based image resolution enhancement techniques have many assumptions, such as limitation of the way to generate low-resolution images and the selection of wavelet functions, which limits their applications in different fields. This paper initially identifies the factors that effectively affect the performance of these techniques and quantitatively evaluates the impact of the existing assumptions. An approach called Optimal Factor Analysis employing the genetic algorithm is then introduced to increase the applicability and fidelity of the existing methods. Moreover, a new Figure of Merit is proposed to assist the selection of parameters and better measure the overall performance. The experimental results show that the proposed approach improves the performance of the selected image resolution enhancement methods and has potential to be extended to other methods.

\end{abstract}


\keywords{super-resolution; interpolation; discrete wavelet transform (DWT).}

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\let\tabcellsep& 	 	 		 
\section[{I. Introduction}]{I. Introduction}\par
esolution has been always an important property in images and videos. High resolution (HR) image/video has a desired and strong demand in most imaging applications as it contains more details that can be crucial in these applications \hyperref[b0]{[1]}. Resolution enhancement based on a single low-resolution (LR) image or multiple LR images has been used for different applications in various fields, such as satellite imaging \hyperref[b1]{[2]}-[5], medical imaging [6], \hyperref[b3]{[7]}, and video enhancement \hyperref[b4]{[8]}- \hyperref[b6]{[10]}.\par
Interpolation is one of the most commonly used techniques for increasing the resolution of a digital image \hyperref[b7]{[11]}- \hyperref[b9]{[13]}. There are four well-known interpolation methods, namely, nearest neighbor, bilinear, bicubic, and Lanczos. Nearest neighbor interpolation is the simplest method where the intensity of the new location point is assigned as that of the old location point which is the nearest neighbor to the new point. Although it is simple to implement, it produces undesirable artefacts, such as distortion of straight edges. In the bilinear interpolation, the value of a new pixel is interpolated linearly using the four nearest neighbour pixels by taking Resolution enhancement techniques in the wavelet domain have attracted more and more investigations to address the problems associated with conventional interpolation methods. Wavelet-Zero Padding (WZP) is relatively simple to implement and is capable of outperforming the conventional interpolation methods but it commonly introduces artefacts such as smoothing and ringing in the neighbourhood of edges in the reconstructed HR image. Addressing this problem, a Cycle-Spinning (CS) based WZP method was proposed \hyperref[b2]{[17]}. Hidden Markov Tree (HMT) based resolution enhancement method is capable of modelling the statistical relationships between coefficients at different scales \hyperref[b13]{[18]}, but the main drawback is that the used Gaussian model does not take into account to keep track of the sign coefficients since the Gaussian is symmetrical around zero and the signs of these coefficients are randomly generated. To reduce this shortcoming, a refined HMT based method was proposed in \hyperref[b22]{[19]}, where the magnitude parameters are estimated using the HMT model, and the sign parameters are estimated based on a higher correlation among the parameters between a high-pass filtered version of the LR image and the high-frequency subbands. A Directional Cycle-Spinning (DCS) method was introduced in \hyperref[b23]{[20]}, where approximates of edge orientation information are derived from a wavelet decomposition of the LR image and used to affect the choice of CS parameters. It can refine better edge orientation and prevent staircase artefacts. More recently, a new dual-tree complex wavelet transform (DT-CWT) technique  {\ref [4]}   
\section[{( ) F}]{( ) F}\par
a weighted average of these pixels \hyperref[b10]{[14]}. Bicubic interpolation preserves fine details better and is more complex than bilinear interpolation where sixteen nearest neighbour pixels are used to estimate the value of the new pixel by taking a weighted average of these points. This method is more efficient and accurate and has become the most popular image interpolation method \hyperref[b11]{[15]}. Lanczos interpolation increases the capability to detect linear features \hyperref[b12]{[16]}. However, the main drawback of most interpolation-based methods is that the produced images suffer from blurring and staircase artefacts. improves Wasnaa Witwit ? , Yitian Zhao ? , Karl Jenkins ? \& Yifan Zhao ? method, the high-frequency coefficients produced by CWT and the input image are interpolated using the Lanczos interpolation. A Demirel-Anbarjafari Super Resolution (DASR) method \hyperref[b24]{[21]} was proposed based on Discrete Wavelet Transform (DWT), where three highfrequency components produced by DWT as well as the input image are interpolated using the bicubic interpolation. An updated DASR technique was proposed in \hyperref[b1]{[2]} with its application in satellite images. Although DWT has been used to preserve the highfrequency details of the image, but downsampling in each of the DWT sub-bands and then the interpolation of the high-frequency sub-bands generate information loss in each of these sub-bands. More recently, a technique based on DWT and stationary wavelet transform (SWT) \hyperref[b25]{[22]} was proposed to correct the estimated high-frequency sub-bands produced using DWT by adding the high-frequency sub-bands obtained by using SWT. that the assumptions they make are not always satisfied for real applications. For example, the detail of a physical object that an optical instrument can reproduce in an image has limits that are mandated by laws of physics, whether formulated by the diffraction equations in the wave theory of light or the Uncertainty Principle for photons in quantum mechanics. There is no such a wellaccepted model can fully describe the underlying mechanism. This mechanism can also be various case by case. In other words, the superior of one method than other methods claimed in the literatures is conditional. Although it has been reported that the performance of resolution enhancement methods can be affected by the methods to produce the lowresolution image, and other factors \hyperref[b12]{[16]}, there is very limited literatures investigating how to utilise these factors to assess and improve the resolution enhancement performance. Addressing this problem, this paper proposes an Optimal Factor Analysis method to increase the applicability and fidelity of the existing methods.\par
Although the authors are aware that machinelearning-based super-resolution methods have attracted more and more interests recently \hyperref[b20]{[23]}- \hyperref[b17]{[28]}, this paper focuses on wavelet-based methods and interpolation methods only. Section 2 initially identifies the important factors that affect the performance and analyses corresponding importance, and then proposes the new method as well as a new Figure of Merit to assist the selection of parameters. Section 3 presents the results of quantitative analysis using the proposed method and associated discussions. Conclusions are presented in the final section. 
\section[{II. Method a) Important Factors}]{II. Method a) Important Factors}\par
Table \hyperref[tab_1]{1} summarises the reviewed waveletbased image resolution enhancement techniques in terms of the way to evaluate their performance. The inconsistency of assumption of the considered factors for each individual technique has been observed. For example, the considered methods make the assumption that the observed LR image is produced by either applying a low-pass filtering and then downsampling, or achieving the low-frequency (LL) sub-band of DWT. For some methods, the description of these factors is either neglected or unclear. The performance of these methods is unknown when such an assumption is not satisfied. A method to compare the resolution enhancement methods in a more comprehensive 
\section[{Global Journal of Computer Science and Technology}]{Global Journal of Computer Science and Technology}\par
Volume XVI Issue III Version I and equitable way is required. Such a method can also be used to further improve the overall performance of existing methods. Each potential factor that affects the performance has been studied one by one. In order to quantitatively evaluate the performance, the widely used Peak-signal-to-noise-ratio (PSNR) has been employed in this paper, and it can be calculated by \hyperref[b0]{(1)} where ?? denotes the maximum fluctuation in the input image. Mean Square Error (MSE) measures the error between the super resolved image ?????? and the original HR image ??????ð??"ð??". It can be calculated by \hyperref[b1]{(2)} where ??,?? denote the width and height of the HR image respectively. 
\section[{i. The mechanism to produce low-resolution images}]{i. The mechanism to produce low-resolution images}\par
It has been identified from the literature review that there are various ways to generate LR image including (a) downsampling of the original HR image through DWT, (b) bicubic interpolation, (c) bilinear interpolation, (d) nearest neighbour, and (e) low-pass filtering. Table \hyperref[tab_2]{2} shows the resulting PSNR values for the Lena image using different resolution enhancement methods by considering different LR image generation methods. Inspection of Table \hyperref[tab_2]{2} shows that WZP with the wavelet function db.9/7 has the best performance among the considered ???? = 10 log 10 (  ii. Wavelet Function There are several well-known wavelet families such as Daubechies (db) (db.1 is also referred as Haar), Symlets (sym), Biorthogonal (bior), Coiflets (coif) etc \hyperref[b18]{[29]}. In this paper, the behaviour of the considered resolution enhancement techniques has been studied for a wide range of wavelet families as well as their various parameters, including db.1-20, sym.2-20, bior.1-6 and coif.1-5. Note that db.9/7 is equivalent to bior4.4 \hyperref[b19]{[30]}. Table \hyperref[tab_3]{3} shows the PSNR values for three test images (Lena, Baboon, and Elaine) using the WZP method with various wavelet functions, where only the parameters producing high PSNR values are shown to save space. The input LR image was produced by downsampling using DWT with db.9/7 wavelet function as suggested in \hyperref[b24]{[21]}. The quantitative results show that considered methods decreases following the increase of scale factor, which indicates that the scale factor is an important factor to be considered for performance assessment. 
\section[{iv. Interpolation Function}]{iv. Interpolation Function}\par
Because of the obvious weakness, in this paper, the nearest method has been neglected, and bilinear, bicubic and Lanczos have been tested. The input LR image has been produced by downsampling using DWT with db.9/7 wavelet function. The PSNR results for Lena image are shown in Table \hyperref[tab_6]{5}, inspection of which indicates that there is no significant difference in performance for different interpolation methods. Moreover, the interpolation method producing the highest PSNR is not consistent for different methods. These observations indicate that the selection of interpolation function for wavelet-based techniques can affect the performance, but not significantly. 
\section[{b) Optimal Factor Analysis}]{b) Optimal Factor Analysis}\par
The behaviour of resolution enhancement methods has been assessed above by varying one factor and fixing other factors, which aims to identify the important factors but it cannot reveal the best technique with the optimal parameter selection. Addressing this challenge, this paper proposes an Optimal Factors Analysis (OFA) approach in order to increase the performance of the existing methods, and also better assess their overall performance.\par
OFA considers a resolution enhancement technique, ?, as a Multi-Input and Multi-Output (MIMO) model, which includes 5 inputs variables: the way to produce LR image ??????(??=1,2,?,??), the scale factor ???? ?? (??=1,2,?,??), the testing image ???? ?? (??=1,2,..,????), the (5) WZP+sym, WZP+coif, and WZP+bior). Three interpolation methods (??=3) were considered, namely bilinear, bicubic and Lanczos. Fig. \hyperref[fig_1]{1} illustrates the performance of the WZP method before and after applying the proposed method, where the LR images were super-resolved from 128×128 to 512×512. The blue and red bars plot the Table \hyperref[tab_7]{6} shows the results including the bestperformed method with its parameter selection, as well as the highest PSNR and RPSNR value for different factors. For the LR image obtained from DWT with db. 9/7 wavelet function, the optimal class corresponding with the optimal interpolation method is WZP using "sym" with bilinear interpolation for the Lena image with scale factor 2. However, for the Baboon and the Elaine images, the best class is WZP using "bior" with bilinear interpolation. For scale factor 4 and 8, the best class with the best interpolation method is WZP using "coif" with Lanczos interpolation for all three images. For This study considered Six methods to generate scale factors 2, 4, and 8 (??=3) and Three testing PSNR values before and after applying OFA respectively. It is clearly shown that the proposed method significantly improves the performance for all 7 ways to produce LR image and all three tested images. over the interpolation methods. This justifies that for almost all papers about wavelet-based techniques, the LR image was produced by either DWT with db. 9/7 wavelet function or low-pass filtering.\par
In order to show the sensitivity for the selection of class of technique with different scale factors, input LR image producing methods and test images, the highest PSNR value for each    However, for the LR images obtained by DWT with db. 9/7, the result of sensitivity analysis is different, as illustrated in Fig. \hyperref[fig_3]{2 (d)}, (e) and (f). The values of std show that the selection of class of technique has significant effect on the results, and it is almost new technique is not important. Another observation is that the above conclusions are almost independent on independent on the scale factor. In other words, the selection of scale factor to demonstrate the superior of a test images due to the fact that Fig. \hyperref[fig_3]{2}   
\section[{III. Conclusions}]{III. Conclusions}\par
The wavelet-based image resolution enhancement techniques have been reviewed in this paper, especially the way to assess the performance. The inconsistency of assumptions has been observed, and for some methods, the description of these assumptions is either neglected or unclear. Due to the fact that the laws of physics to generate LR images are unclear and also various case by case, the current ways to assess performance assumptions may result in a biased conclusion. The importance of each factor has then been analysed by varying this factor and fixing other factors. It has been revealed that the way of producing LR image, the variation of wavelet family and its wavelet functions, and the scale factor can substantially affect the performance of techniques. \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{fig_4}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.18159784560143627\textwidth}P{0.2563734290843806\textwidth}P{0.07630161579892279\textwidth}P{0.06409335727109515\textwidth}P{0.0656193895870736\textwidth}P{0.20601436265709155\textwidth}}
Year 2016\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
12\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{3}{l}{A major limitation of most above methods is}\tabcellsep \tabcellsep \tabcellsep \\
)\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
(\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \multicolumn{2}{l}{assessment}\tabcellsep \tabcellsep \\
Techniques\tabcellsep Input LR Image\tabcellsep Scale Factor\tabcellsep Interpolation Method\tabcellsep Wavelet Function\tabcellsep Test Image\\
WZP-CS [17]\tabcellsep LL sub-band of DWT\tabcellsep 2 \& 4\tabcellsep N/A\tabcellsep Db.9/7\tabcellsep Lena, Elaine, Baboon, and Peppers\\
WZP-DCS [20]\tabcellsep Low-pass filtering and downsampling\tabcellsep 2 \& 4\tabcellsep N/A\tabcellsep Db.9/7\tabcellsep Lena, Elaine, Baboon, and Peppers\\
HMT [18]\tabcellsep HR image Downsampling of\tabcellsep N/A\tabcellsep N/A\tabcellsep N/A\tabcellsep Lena\\
HMT [5]\tabcellsep Downsampling of HR image\tabcellsep 2\tabcellsep N/A\tabcellsep N/A\tabcellsep Lena\\
HMT [19]\tabcellsep low-pass filtering and downsampling\tabcellsep 2 \& 4\tabcellsep N/A\tabcellsep Db.9/7\tabcellsep Lena, Elaine, Baboon, and Peppers\\
CWT [3]\tabcellsep LL sub-band of DWT\tabcellsep 2 \& 4\tabcellsep Bicubic\tabcellsep N/A\tabcellsep 5 Satellite Images\end{longtable} \par
 
\caption{\label{tab_1}Table 1 : Summary of different wavelet-based resolution enhancement techniques in terms of performance}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{}
\end{longtable} \par
  {\small\itshape [Note: results for Lena image using different techniques for resolution enhancement from 128×128 to 512×512 for several LR image generation methods methods for the input image produced by DWT with the wavelet function db.9/7. For the LR images obtained by DWT (Haar), bicubic, bilinear interpolations and lowpass filtering methods, the bicubic interpolation method has the best performance, but for the LR images produced by the nearest neighbor, the bilinear interpolation technique has the best performance. These observations clearly indicate that the method to produce LR images has significant effect on the performance of different techniques.]} 
\caption{\label{tab_2}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.16346153846153846\textwidth}P{0.11442307692307692\textwidth}P{0.01362179487179487\textwidth}P{0.0953525641025641\textwidth}P{0.06538461538461539\textwidth}P{0.39775641025641023\textwidth}}
DT-CWT [4]\tabcellsep Downsampling of HR image\tabcellsep 4\tabcellsep Lanczoc\tabcellsep N/A\tabcellsep 1 Satellite Image (Washington DC)\\
DASR [21]\tabcellsep LL sub-band of DWT\tabcellsep 4\tabcellsep Bicubic\tabcellsep Db.9/7\tabcellsep Lena, Elaine, Baboon, and Peppers\\
DWT-Difference [2]\tabcellsep \tabcellsep 4\tabcellsep Bicubic\tabcellsep Db.9/7\tabcellsep 5 Satellite Images\\
DWT-SWT [22]\tabcellsep \tabcellsep 4\tabcellsep Bicubic\tabcellsep Db.9/7\tabcellsep Lena, Elaine, Baboon, and Peppers\\
DWT-SWT [6]\tabcellsep \tabcellsep 4\tabcellsep Bicubic\tabcellsep N/A\tabcellsep Lena, Elaine, Head, and Brain\end{longtable} \par
 
\caption{\label{tab_3}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_4}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.009042553191489361\textwidth}P{0.8409574468085107\textwidth}}
\tabcellsep Year 2016\\
\tabcellsep 15\\
1\tabcellsep Volume XVI Issue III Version I\\
\tabcellsep )\\
\tabcellsep F\\
\tabcellsep (\\
\tabcellsep Global Journal of Computer Science and Technology\end{longtable} \par
 
\caption{\label{tab_5}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.85\textwidth}}
9/7 for resolution enlargement factor from\end{longtable} \par
  {\small\itshape [Note: ? (???? ?? ,???? ?? ,???? ?? ,???? ?? ,???? ?? ) (3)Depending on the value of ??,??,??,??, and ??, Eq.]} 
\caption{\label{tab_6}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6} \par 
\begin{longtable}{P{0.012913727618014108\textwidth}P{0.009224091155724362\textwidth}P{0.13374932175800328\textwidth}P{0.14343461747151381\textwidth}P{0.15265870862723818\textwidth}P{0.13928377645143789\textwidth}P{0.13005968529571352\textwidth}P{0.12867607162235484\textwidth}}
Testing\tabcellsep Scale\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Methods to produce LR image}\tabcellsep \tabcellsep \\
image\tabcellsep factor\tabcellsep DWT by DB.9/7\tabcellsep DWT by Haar\tabcellsep Bicubic\tabcellsep Bilinear\tabcellsep Nearest\tabcellsep Low-pass\\
\tabcellsep 2\tabcellsep WZP(sym20)\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep WZP(sym18)\tabcellsep WZP(sym18)\\
\tabcellsep \tabcellsep Bilinear\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Bilinear\tabcellsep Bilinear\\
\tabcellsep \tabcellsep 32.98(1.1762)\tabcellsep 32.63(1.0221)\tabcellsep 32.48(1.0237)\tabcellsep 30.85(1.0218)\tabcellsep 31.22(1.1321)\tabcellsep 31.18(1.1233)\\
\tabcellsep 4\tabcellsep WZP(coif2)\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep WZP(sym18)\tabcellsep WZP(sym18)\\
Lena\tabcellsep \tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Bicubic\tabcellsep Lanczos\\
\tabcellsep \tabcellsep 26.88(1.1945)\tabcellsep 26.56(1.0097)\tabcellsep 26.58(1.0117)\tabcellsep 25.89(1.0126)\tabcellsep 25.40(1.0244)\tabcellsep 26.45(1.0305)\\
\tabcellsep 8\tabcellsep WZP(coif4)\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep WZP(sym8)\tabcellsep WZP(sym9)\\
\tabcellsep \tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Bilinear\tabcellsep Bicubic\\
\tabcellsep \tabcellsep 23.14(1.2008)\tabcellsep 23.05(1.0058)\tabcellsep 23.09(1.0078)\tabcellsep 22.64(1.0096)\tabcellsep 21.76(1.0051)\tabcellsep 22.35(1.0035)\\
\tabcellsep 2\tabcellsep WZP(bior4.4)\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep WZP(sym13)\tabcellsep WZP(sym6)\tabcellsep WZP(sym18)\\
\tabcellsep \tabcellsep Bilinear\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Bilinear\tabcellsep Bilinear\tabcellsep Bilinear\\
\tabcellsep \tabcellsep 30.09(1.0733)\tabcellsep 29.65(1.0035)\tabcellsep 29.68(1.0088)\tabcellsep 28.98(1.0100)\tabcellsep 28.09(1.0375)\tabcellsep 29.21(1.0546)\\
\tabcellsep 4\tabcellsep WZP(coif2)\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep WZP(sym18)\tabcellsep WZP(sym18)\\
Baboon\tabcellsep \tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Bilinear\tabcellsep Bicubic\\
\tabcellsep \tabcellsep 26.44(1.0903)\tabcellsep 26.34(1.0028)\tabcellsep 26.40(1.0052)\tabcellsep 26.04(1.0063)\tabcellsep 25.25(1.0257)\tabcellsep 26.22(1.0119)\\
\tabcellsep 8\tabcellsep WZP(coif4)\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep WZP(bior5.5)\tabcellsep WZP(bior3.1)\tabcellsep WZP(sym6)\\
\tabcellsep \tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Bilinear\tabcellsep Bilinear\\
\tabcellsep \tabcellsep 24.22(1.1063)\tabcellsep 24.06(1.0030)\tabcellsep 24.10(1.0050)\tabcellsep 23.86(1.0066)\tabcellsep 22.76(1.0219)\tabcellsep 23.49(1.0038)\\
\tabcellsep 2\tabcellsep WZP(bior4.4)\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep WZP(sym6)\tabcellsep WZP(sym18)\\
\tabcellsep \tabcellsep Bilinear\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Bilinear\tabcellsep Lanczos\\
\tabcellsep \tabcellsep 34.96(1.0824)\tabcellsep 34.54 (1.0043)\tabcellsep 34.56(1.0073)\tabcellsep 33.56(1.0084)\tabcellsep 32.71(1.0402)\tabcellsep 33.73(1.0652)\\
\tabcellsep 4\tabcellsep WZP(coif2)\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep WZP(sym18)\tabcellsep WZP(sym18)\\
Elaine\tabcellsep \tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Bicubic\tabcellsep Lanczos\\
\tabcellsep \tabcellsep 30.64(1.1785)\tabcellsep 30.42 (1.0090)\tabcellsep 30.49(1.0096)\tabcellsep 29.70(1.0111)\tabcellsep 29.35(1.0259)\tabcellsep 30.39(1.0323)\\
\tabcellsep 8\tabcellsep WZP(coif4)\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep Interpolation\tabcellsep WZP(sym17)\tabcellsep WZP(sym17)\\
\tabcellsep \tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Lanczos\tabcellsep Bicubic\tabcellsep Bicubic\\
\tabcellsep \tabcellsep 26.58(1.2371)\tabcellsep 26.60 (1.0121)\tabcellsep 26.63(1.0124)\tabcellsep 25.89(1.0139)\tabcellsep 25.26(1.0069)\tabcellsep 26.08(1.0073)\end{longtable} \par
  {\small\itshape [Note: the LR image obtained from DWT with Haar, bicubic, and bilinear, the best technique with the highest PSNR value is Lanczos interpolation for most of the cases. For the LR image produced by nearest and low-pass filtering, the best class is WZP using "sym" for almost all cases. These observations conclude that, for the LR image obtained from DWT with db. 9/7 wavelet function, nearest and low-pass filtering, the wavelet-based techniques have the biggest potential to outperform the conventional interpolation methods, due the fact that they have relatively large RPSNR values. For the LR image obtained from Haar, bicubic, and bilinear, the wavelet-based methods have no significant advantages]} 
\caption{\label{tab_7}Table 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_8}Table 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.5903940886699508\textwidth}P{0.0041871921182266006\textwidth}P{0.03628899835796388\textwidth}P{0.01814449917898194\textwidth}P{0.025123152709359605\textwidth}P{0.03489326765188834\textwidth}P{0.05024630541871921\textwidth}P{0.03489326765188834\textwidth}P{0.05024630541871921\textwidth}P{0.005582922824302134\textwidth}}
\multicolumn{10}{l}{performance moderately. 19 Year 2016}\\
\tabcellsep \tabcellsep Lena\tabcellsep \tabcellsep \tabcellsep \tabcellsep Baboon\tabcellsep \tabcellsep Elaine\\
Scale\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep Low-\tabcellsep \multicolumn{2}{l}{DWT by db.}\tabcellsep \tabcellsep DWT by db.\tabcellsep Low-\tabcellsep DWT by db.\\
Factor\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep Low-pass\tabcellsep \tabcellsep \tabcellsep \tabcellsep )\\
\tabcellsep \tabcellsep pass\tabcellsep \tabcellsep 9/7\tabcellsep \tabcellsep 9/7\tabcellsep pass\tabcellsep 9/7\tabcellsep ( F\\
\multicolumn{5}{l}{2 techniques have no pronounced improvements over 2.50 2.16 4 0.88 1.92 conventional interpolation methods. All these observations conclude that in order to assess more}\tabcellsep 1.27 0.43\tabcellsep 0.83 0.99\tabcellsep 1.71 0.97\tabcellsep 1.05 2.01\\
8 comprehensively\tabcellsep and\tabcellsep 0.16 equitably\tabcellsep for\tabcellsep 1.70 resolution\tabcellsep 0.07\tabcellsep 1.03\tabcellsep 0.28\tabcellsep 2.27\\
\multicolumn{5}{l}{16 enhancement techniques, variation of LR image 0.03 1.40 generation method, scale factor, and wavelet functions}\tabcellsep 0.03\tabcellsep 0.92\tabcellsep 0.04\tabcellsep 1.91\\
\multicolumn{5}{l}{must be considered, otherwise observed performance}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{3}{l}{could be limited and biased.}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_10}}\end{figure}
 			\footnote{© 2016 Global Journals Inc. (US)} 			\footnote{© 2016 Global Journals Inc. (US) 1} 		 		\backmatter   			 
\subsection[{IV. Acknowledgements}]{IV. Acknowledgements}\par
This work was supported by the Through-life Engineering Services Centre. 			  			  				\begin{bibitemlist}{1}
\bibitem[Azam et al. (2014)]{b12}\label{b12} 	 		‘A State-ofthe-art Review on Wavelet Based Image Resolution Enhancement Techniques: Performance Evaluation Criteria and Issues’.  		 			S Azam 		,  		 			F Tuz Zohra 		,  		 			M M Islam 		.  	 	 		\textit{Int. J. Image, Graph. Signal Process}  		Aug. 2014. 6  (9)  p. .  	 
\bibitem[Parker et al. (1983)]{b9}\label{b9} 	 		‘Comparison of Interpolating Methods for Image Resampling’.  		 			J A Parker 		,  		 			R V Kenyon 		,  		 			D E Troxel 		.  	 	 		\textit{IEEE Trans. Med. Imaging}  		Mar. 1983. 2  (1)  p. .  	 
\bibitem[Keys (1981)]{b8}\label{b8} 	 		‘Cubic convolution interpolation for digital image processing’.  		 			R Keys 		.  	 	 		\textit{IEEE Trans. Acoust}  		Dec. 1981. 29  (6)  p. .  	 
\bibitem[Hou and Andrews (1978)]{b7}\label{b7} 	 		‘Cubic splines for image interpolation and digital filtering’.  		 			Hsieh Hou 		,  		 			H Andrews 		.  	 	 		\textit{IEEE Trans. Acoust}  		Dec. 1978. 26  (6)  p. .  	 
\bibitem[Demirel and Anbarjafari ()]{b1}\label{b1} 	 		‘Discrete Wavelet Transform-Based Satellite Image Resolution Enhancement’.  		 			H Demirel 		,  		 			G Anbarjafari 		.  	 	 		\textit{IEEE Trans. Geosci. Remote Sens}  		1997-2004, Jun. 2011. 49  (6) .  	 
\bibitem[Tang et al. (2016)]{b14}\label{b14} 	 		‘Example-based super-resolution via social images’.  		 			Y Tang 		,  		 			H Chen 		,  		 			Z Liu 		,  		 			B Song 		,  		 			Q Wang 		.  	 	 		\textit{Neurocomputing}  		Jan. 2016. 172 p. .  	 
\bibitem[Gonzalez et al. ()]{b18}\label{b18} 	 		 			R C Gonzalez 		,  		 			R E Woods 		,  		 			S L Eddins 		.  		\textit{Digital Image Processing Using MATLAB},  				2004. Pearson Education.  	 
\bibitem[Gonzalez and Woods ()]{b10}\label{b10} 	 		 			R C Gonzalez 		,  		 			R E Woods 		.  		\textit{Digital image processing},  				 (NJ)  		2007. Prentice Hall.  	 
\bibitem[Antonini et al. (1992)]{b19}\label{b19} 	 		‘Image coding using wavelet transform’.  		 			M Antonini 		,  		 			M Barlaud 		,  		 			P Mathieu 		,  		 			I Daubechies 		.  	 	 		\textit{IEEE Trans. Image Process}  		Apr. 1992. 1  (2)  p. .  	 
\bibitem[Kinebuchi et al.]{b13}\label{b13} 	 		\textit{Image interpolation using wavelet based hidden Markov trees},  		 			K Kinebuchi 		,  		 			D D Muresan 		,  		 			T W Parks 		.  		 	 	 (in 2001 IEEE International) 
\bibitem[Demirel and Anbarjafari (2011)]{b25}\label{b25} 	 		‘IMAGE Resolution Enhancement by Using Discrete and Stationary Wavelet Decomposition’.  		 			H Demirel 		,  		 			G Anbarjafari 		.  	 	 		\textit{IEEE Trans. Image Process}  		May 2011. 20  (5)  p. .  	 
\bibitem[
			A
		 ()]{b22}\label{b22} 	 		‘Image Resolution Enhancement using Wavelet Domain Hidden Markov Tree and Coefficient Sign Estimation’.  		 			A 		.  	 	 		\textit{2007 IEEE International Conference on Image Processing},  				2007. p. .  	 
\bibitem[Vlachos (2005)]{b23}\label{b23} 	 		‘Image resolution upscaling in the wavelet domain using directional cycle spinning’.  		 			T Vlachos 		.  	 	 		\textit{J. Electron. Imaging}  		Oct. 2005. 14  (4)  p. 40501.  	 
\bibitem[Anbarjafari and Demirel (2010)]{b24}\label{b24} 	 		‘Image Super Resolution Based on Interpolation of Wavelet Domain High Frequency Subbands and the Spatial Domain Input Image’.  		 			G Anbarjafari 		,  		 			H Demirel 		.  	 	 		\textit{ETRI J}  		Jun. 2010. 32  (3)  p. .  	 
\bibitem[Liang et al. (2016)]{b20}\label{b20} 	 		‘Incorporating image priors with deep convolutional neural networks for image super-resolution’.  		 			Y Liang 		,  		 			J Wang 		,  		 			S Zhou 		,  		 			Y Gong 		,  		 			N Zheng 		.  	 	 		\textit{Neurocomputing}  		Jun. 2016. 194 p. .  	 
\bibitem[Shen et al. (2014)]{b17}\label{b17} 	 		‘Interactive Segmentation Using Constrained Laplacian Optimization’.  		 			J Shen 		,  		 			Y Du 		,  		 			X Li 		.  	 	 		\textit{IEEE Trans. Circuits Syst. Video Technol}  		Jul. 2014. 24  (7)  p. .  	 
\bibitem[Shen et al. (2014)]{b16}\label{b16} 	 		‘Lazy Random Walks for Superpixel Segmentation’.  		 			Jianbing Shen 		,  		 			Yunfan Du 		,  		 			Wenguan Wang 		,  		 			Xuelong Li 		.  	 	 		\textit{IEEE Trans. Image Process}  		Apr. 2014. 23  (4)  p. .  	 
\bibitem[Li et al. (2015)]{b15}\label{b15} 	 		‘Learning local Gaussian process regression for image super-resolution’.  		 			J Li 		,  		 			Y Qu 		,  		 			C Li 		,  		 			Y Xie 		,  		 			Y Wu 		,  		 			J Fan 		.  	 	 		\textit{Neurocomputing}  		Apr. 2015. 154 p. .  	 
\bibitem[Lu et al. (2015)]{b3}\label{b3} 	 		‘MR image superresolution via manifold regularized sparse learning’.  		 			X Lu 		,  		 			Z Huang 		,  		 			Y Yuan 		.  	 	 		\textit{Neurocomputing}  		Aug. 2015. 162 p. .  	 
\bibitem[Ning and Gao (2013)]{b5}\label{b5} 	 		‘Multi-frame image superresolution reconstruction using sparsecooccurrence prior and sub-pixel registration’.  		 			B Ning 		,  		 			X Gao 		.  	 	 		\textit{Neurocomputing}  		Oct. 2013. 117 p. .  	 
\bibitem[Maeland ()]{b11}\label{b11} 	 		‘On the comparison of interpolation methods’.  		 			E Maeland 		.  	 	 		\textit{IEEE Trans. Med. Imaging}  		1988. 7  (3)  p. .  	 
\bibitem[Zhao et al. (2016)]{b21}\label{b21} 	 		‘Single Image Super-Resolution via Blind Blurring Estimation and Dictionary Learning’.  		 			X Zhao 		,  		 			Y Wu 		,  		 			J Tian 		,  		 			H Zhang 		.  	 	 		\textit{Neurocomputing}  		Jun. 2016.  	 
\bibitem[Sung Cheol Park et al. (2003)]{b0}\label{b0} 	 		‘Super-resolution image reconstruction: a technical overview’.  		 			Min Kyu Sung Cheol Park 		,  		 			Moon Gi Park 		,  		 			Kang 		.  	 	 		\textit{IEEE Signal Process. Mag}  		May 2003. 20  (3)  p. .  	 
\bibitem[Anbarjafari et al. (2015)]{b4}\label{b4} 	 		‘Video resolution enhancement by using discrete and stationary wavelet transforms with illumination compensation’.  		 			G Anbarjafari 		,  		 			S Izadpanahi 		,  		 			H Demirel 		.  	 	 		\textit{Signal, Image Video Process},  				Jan. 2015. 9 p. .  	 
\bibitem[Zhang et al. (2012)]{b6}\label{b6} 	 		‘Video super-resolution with 3D adaptive normalized convolution’.  		 			K Zhang 		,  		 			G Mu 		,  		 			Y Yuan 		,  		 			X Gao 		,  		 			D Tao 		.  	 	 		\textit{Neurocomputing}  		Oct. 2012. 94 p. .  	 
\bibitem[Temizel and Vlachos ()]{b2}\label{b2} 	 		‘Wavelet domain image resolution enhancement using cycle-spinning’.  		 			A Temizel 		,  		 			T Vlachos 		.  	 	 		\textit{Electron. Lett}  		2005. 41  (3)  p. 119.  	 
\end{bibitemlist}
 			 		 	 
\end{document}
