Linearly uncorrelated principal component and deep convolutional image deblurring for natural images

IET Image ProcessingVolume 13, Issue 1 p. 49-56 Research ArticleFree Access Linearly uncorrelated principal component and deep convolutional image deblurring for natural images Amudha Jeyaprakash, Corresponding Author Amudha Jeyaprakash a_jeyaprakash@yahoo.com.sg EEE Department, Dr. Mahalingam College of Engineering and Technology, Pollachi, TN, 642003 IndiaSearch for more papers by this authorSudhakar Radhakrishnan, Sudhakar Radhakrishnan ECE Department, Dr. Mahalingam College of Engineering and Technology, Pollachi, TN, 642003 IndiaSearch for more papers by this author Amudha Jeyaprakash, Corresponding Author Amudha Jeyaprakash a_jeyaprakash@yahoo.com.sg EEE Department, Dr. Mahalingam College of Engineering and Technology, Pollachi, TN, 642003 IndiaSearch for more papers by this authorSudhakar Radhakrishnan, Sudhakar Radhakrishnan ECE Department, Dr. Mahalingam College of Engineering and Technology, Pollachi, TN, 642003 IndiaSearch for more papers by this author First published: 01 January 2019 https://doi.org/10.1049/iet-ipr.2018.5209Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Blind image deblurring of natural images still remains a demanding task. The traditional methods, pre-processes the uniform and non-uniform images with a deblurring algorithm and employs a low-rank prior algorithm. The rich textures do not possess enough similar patches in the deblurring process and this loss results in noisy images. Also, computational efficiency gets compromised during the performance of the succeeding process. In this study, the authors propose a novel method called, linearly uncorrelated principal component and deep convolution (LUPC-DC) for deblurring natural images. The natural images are first de-correlated with which good similar patches are extracted to generate a low-rank matrix by linearly uncorrelated principal component (PC) extraction. Then, the deep convolutional neural network model jointly extracts good similar patches and deblurs the first PCs. Eventually, good similar patches in the last PCs are suppressed using Hard Thresholding for computational efficiency. Analysis of concurrence performance of the algorithm confirms the viability of this method theoretically. In addition, simulation results and performance evaluations of image quality metrics are provided to assess the effectiveness of the proposed method. Moreover, the proposed method provides improvement in the peak-signal-to-noise ratio rate, success rate and reduction in the computation time for image deblurring. 1 Introduction Image deblurring has been observed remarkable advancements in the vision and graphics association. The process of image deblurring involves removing blurring artefacts from natural images. The objective of image deblurring is to retrieve a comprehensible image and a blur kernel from a blurred input. A novel blind image deblurring called Image Prior was investigated in [1] based on an elastic-net regularisation of singular values measured from similar patches of an image. Followed by this, an efficient numerical optimisation method was then designed. In Image Prior, an elastic-net based model was presented for blind image deblurring. The Image Prior was constructed with the aid of weighted nuclear norm. This weighted nuclear norm, in turn, provided minimum shrinkage for large singular values that in turn helped in conserving paramount structures. In addition, a convex F-norm was then designed to achieve a stable and robust solution. The Image Prior also provides clear images over blurred images, that helped in the efficient estimation of the kernel when compared with the conventional Maximum A Posterior framework. Both quantitative and qualitative experiments show that the Image Prior method performed favourably in terms of peak-signal-to-noise ratio (PSNR). Although Image Prior was able to help guess blur kernels, images possessing rich textures do not possess enough similar patches. As a result, without good similar patches, the low-rank matrix was not said to be generated, resulting in noisy images. Potential solution addressed in the work is to extract good similar patches by applying principal component (PC) analysis and therefore resulting in denoise images. Approximation of matrices based on low rank has been successfully applied to several fields of research in recent years. Low rank matrix approximation (LRMA) [2] for deblurring directly applied a low rank mechanism to a blurry input image. This application of low rank mechanism had a significant effect that in turn minimised the blur without the aid of kernel information. Based on these properties, LRMA for deblurring introduced an enhanced image deblurring method by integrated low rank prior to similar patches from both the blurry image and its gradient map. In addition, the method also used a weighted nuclear norm minimisation to increase the efficiency of low rank prior to image deblurring. This was performed by maintaining the superior edges and discarding fine texture and edges in intermediate images. With this, the method was proved to be efficient in terms of PSNR, structural similarity and kernel similarity. Despite improvement being observed in the noise ratio, the computational time involved in deblurring was not focused. Potential solution addressed in this work is to introduce a machine learning technique called deep convolutional neural networks (DCNNs) and Hard threshold denoising to reduce the computational time involved during the deblurring of natural images. Image deblurring applications extend from pattern recognition to human face recognition and so on. In [3], point spread functions (PSFs) represented by a linear combination of intrinsic and orthogonal face images, resulting in the improvement of face recognition. On the other hand, subjective scores were used as a basis to measure the performance of deblurring algorithms [4]. Followed by deblurring, quality enhancement based on Gray level co-occurrence matrix was designed to evaluate the loss of naturalness of the texture caused by deblurring. Yet another method for efficient restoration, based on, convolutional sparse coding was investigated in [5] with the objective of approaching the solution in an optimal manner. In this paper, we propose a novel algorithm for natural images with linearly uncorrelated PC (LUPC) extraction and DCNNs. This method is called as linearly uncorrelated principal component and deep convolution (LUPC-DC) deblurring for natural images. The natural images are first de-correlated with which good similar patches are extracted to generate a low-rank matrix by means of LUPC Extraction. Then, the DCNN models jointly extract the good similar patches and deblur the first PCs. Eventually, good similar patches in the last PCs are suppressed using Hard thresholding technique, for computational efficiency. The enhancement brought by the proposed method is validated by the processing results of natural images. In this work, we de-correlate the noisy natural images into good similar patches using LUPC extraction, to generate a low-rank matrix. Followed by this, the good similar patches are decomposed into first 'i' components and remaining '' components. Then we apply DCNN to the first 'i' components to deblur the preserve the first 'i' components. During reconstruction, feature maps are generated and the generated feature map is used during deblurring. Finally, to the remaining '' components, the optimal Hard threshold is applied to obtain the restored original image with less noise. Simulation studies have been carried out in order to test the efficiency of the proposed method with the help of PSNR, success rate and computational time. The proposed method is also tested by taking a different combination of images and distance factor. In addition, the result is also compared with some of the existing state-of-the-art image deblurring methods. The result shows that there is a substantial improvement in the PSNR, success rate and computational time measures for natural images. The remaining of the paper is organised as follows. In Section 2, a short overview of image deblurring techniques and methods are presented. In Section 3, the process of image deblurring using LUPC-DC with DCNN and the adaptive threshold for image deblurring is investigated. In Section 4, experimental settings are provided, followed by which the experimental results of the proposed method are discussed and compared with methods. Finally, Section 5 concludes the paper. 2 Related works Communications through image and video have become a significant aspect of our everyday life. It is highly essential to apprehend accurate and clean images for better image comprehension and understanding and presentation. However, several images acquiring devices repeatedly present noise during image acquiring process. Weighted bilateral filter through Curvlet transform [6] provided insight into not only providing the user with image restoration but also an understanding of the image. Total variation minimisation approach was presented in [7] to denoise and deblur the Gold Immuno Chromatographic Strip images. However, the accuracy with which the image was being deblurred remained a major concern. To address this issue, a wavelet-domain hierarchical blur model was introduced in [8]. A statistics of Natural Stochastic Textures was presented in [9] for image restoration and enhancement. With a vital constituent of machine vision, in recent years, medical image fusion has attracted several researchers. It is a notable technology for diagnosing and investigations in the area of medicinal instrumentation and calculation. A total variation model for medical image fusion and denoising was presented in [10]. However, with the handcrafted parameter tuning, satisfactory estimation was not said to be achieved. To address this issue, iteration-wise generalised shrinkage thresholding was presented in [11] to improve the visual quality of images. Despite improvement found in the visual quality of images, inconsistent recovery of sparse images resulted in the corruption of spectral similarity. To provide a solution, an intra-clustering filtering scheme was presented in [12] that efficiently restored the similarity of spectral values in each spatial cluster. In recent years, video capture has received wide popularity with the extensive accessibility of digital cameras. However, at the same time, motion blur is inevitable in natural video capture due to several factors namely shake in camera, the motion of the object during exposure. In [13], a super pixel matching was presented to substitute with a blurry image. This, in turn, had significant improvement that in turn reconstructed sharp video frames from the blurred frame. Yet another, Text-specific Multiscale Dictionaries was designed in [14] that achieved deblurring results with significant visual quality. A technique for denoising and restoration of sparse images was designed in [15] on the basis of a gradient-descent algorithm. The objective of using this gradient-descent algorithm was that the uncorrupted pixels were not changed. However, corrupted pixels were identified and discarded in an iterative manner with the help of a gradient of sparsity measure. With the corrupted pixels identified and discarded, the gradient algorithm was then used to reconstruct the original image. The deep neural network was applied in [16] with the objective of extracting multi-scale and the most discriminating features. In [17], row column sparse representations were made to improve the visual quality through a singular value decomposition. Weiner filtering was applied in [18] to obtain the restored images that not only resulted in the improved resolution but also reduced the noise level. In this paper, we present an image deblurring for natural images based on the machine learning algorithm. First, we use the LUPC to segregate the PCs. Following this, we applied the DCNN to the first PC for image denoising and deblurring. Finally, we use the remaining PCs to obtain the original restored image using Optimal Hard Threshold. 3 LUPC and deep convolution In this section, an integrated denoising and deblurring method called, linearly uncorrelated principal component and deep convolution (LUPC-DC) for image deblurring using natural images is presented. Machine learning denoising and deblurring is considerably used in image processing applications because machine learning techniques allow users to identify its hidden insights without being explicitly programmed and are able to adapt independently. Also, while processing natural images, machine learning techniques are considered to be computationally efficient. Fig. 1 shows the block diagram of LUPC-DC for image deblurring using natural images. The first 'i' PCA components comprise most of the total energy of a natural image, and the remaining '' PCA components principally include noise. If deblurring is accomplished on these noisy components, then it will further increase the noise and results in high computational time in processing the image. Therefore, as shown in Fig. 1, a fast and efficient machine learning technique, called, deep convolutional neural network (DCNN) is used to cooperatively denoise and deblur only the first 'i' PCA components. These 'i' PCA components are initially extracted based on the linear uncorrelated model. The noise and blur present in the first 'i' PCA components are then removed by applying a machine learning technique called, deep convolutional neural network model. In the remaining '' PCA components, a Hard thresholding is applied to remove the noise. The elaborate description of the method is given in the forthcoming sections. Fig. 1Open in figure viewerPowerPoint Block diagram of LUPC-DC 3.1 LUPC extraction In this section, the extraction of PCs using linear uncorrelated for natural images is discussed. Let us consider the process of the deblurring with the assumption that the blurring of the columns in the image is independent of the blurring of the rows. Then, the blurring process is modelled by dual blurring matrices, and and is represented as (1)From the above matrix (1), represents the real numbers and n represents the length of linear blur in terms of pixels. Then, the relation between the original image P and the blurred image B is expressed by the following matrix equation: (2) (3) (4)From (2) and (3), , and represent, respectively, the blurred image, the original image and the additive noise present in the image with representing the PSF of the blurring operator. The motive behind blind image deblurring for natural images is to evaluate the original image based on the partial knowledge of the features of and to acquire the evaluation of of the original image. The pseudo code representation of PC extraction is given in Algorithm 1 (see Fig. 2). Fig. 2Open in figure viewerPowerPoint Algorithm 1: PC extraction algorithm As given in Algorithm 1 (Fig. 2), mathematically, the transformation is defined by a set of vector of weights that maps each row vector of B to a new vector of PC outcomes . It is mathematically represented as (5)Equation (5) is formulated in such a manner that the individual outputs (i.e. components) of O considered over the natural images individually inherit the maximal probable variance from B, with each loading vector constrained to be a unit vector. Then, the first component is mathematically expressed as given below: (6)From (6), the first PC is obtained based on the product of the first blur image row value representation and its corresponding weight . Further components or the is then obtained as (7)The focus here remains that only the first PC extracted from the natural images is subjected to DCNN, whereas the remaining components are subjected to Hard thresholding. 3.2 Deep convolutional neural network With the PCs extracted, the next step is to perform denoising and deblurring using the DCNN model. The DCNN model for deblurring comprises of a number of convolutional and subsampling layers (i.e. first PC ) followed by fully connected layers i.e. remaining layers (i.e. remaining PC ). The pseudo code representation of blind deep convolutional is given in Algorithm 2 (see Fig. 3). Fig. 3Open in figure viewerPowerPoint Algorithm 2: Blind deep convolutional algorithm As given Algorithm 2 (Fig. 3), the input to deep convolutional layer is a image, where r and c represent the row and the column of the PC, respectively, and C represents the total channels (i.e. for an RGB natural image, the value of ). In DCNN model, the matrix representation of natural images is also referred to as the filter. The filter now slides over the first PC resulting in a feature map. Fig. 4 shows the example of convolutional operation carried out from the resultant first PC. Fig. 4Open in figure viewerPowerPoint Example of convolutional layer As shown in the figure, with the first component image given as input, a feature map is then obtained through repeated iterations by applying a non-linear function. The non-linear function used in the LUPC-DC method is rectified linear unit (RLU). The DCNN model for deblurring includes several layers combine convolutions (i.e. components) to the RLU. The purpose of using RLU for DCNN model is that it involves a non-linear operation. On the other hand, convolution is a linear operator. Therefore, by applying the non-linear RLU, computational time is said to be reduced during deblurring. The mathematical model is expressed as (8) (9)From (8) and (9), and correspond to the convolutional layer of the and layers for the first PC, with 'l' and 'w' representing the layer and weight of each layer, respectively. 3.3 Hard threshold denoising In Section 3.2, cooperative denoise and deblur of the first PCs is performed. The noise present in the remaining PCs is removed using Hard thresholding. To suppress the noise present in the remaining '' components, Hard thresholding is applied. The pseudo code representation of Hard threshold denoising is given in Algorithm 3 (see Fig. 5). Fig. 5Open in figure viewerPowerPoint Algorithm 3: Hard threshold denoising As provided in Algorithm 3 (Fig. 5), for remaining and for total C channels given as input, noisy and filtered images are obtained. To obtain this, a threshold has to be identified. This is performed by applying an adaptive threshold denoising algorithm. The algorithm is mathematically represented as given below: (10) (11)From (10), represents the threshold with representing the noisy image and represents the filtered image. The selection of threshold plays an important role in noise removal. Selection of large threshold value results in irrelevant denoising of a natural image. On the other hand, selection of small threshold value does not perform proper denoising, or relevant denoising is not said to be performed. Hence, the value of is arrived at using optimal Hard threshold. This optimal Hard threshold is mathematically expressed as given below: (12)From (12), the significant value of the threshold is arrived at based on the length of the input n (i.e. components) and variance of noise represented by . Finally, by combining both the LUPC extraction and Hard threshold denoising for the first i components and remaining components, restored natural images are said to be obtained. 4 Experiments In this section, a series of experiments are conducted to verify the efficiency and effectiveness of our deblurring algorithm. For comparison, Image Prior [1] and LRMA [2] Gradient Projection Method [7] and Coupled Learning Algorithm [3] are chosen for deblurring. Tests are conducted using UPenn Natural Image Database [19]. The natural images are selected from UPenn Natural Image Database, that include many snapshots of what a human observer might conceivably look at, such as images of the horizon and detailed images of the ground, trees, bushes, and baboon sand the defined testing method results are compared with the existing method. In order to perform deblurring of natural images uses the proposed LUPC-DC method and comparison with four other existing methods, Image Prior [1], LRMA [2], Gradient Projection Method [7] and Coupled Learning Algorithm [3] using UPenn Natural Image Database. The UPenn Natural Image Database is accessible at http://tofu.psych.upenn.edu/ [20]. The database includes a standard gallery program for viewing the images. This, in turn, makes browsing and downloading individual images easy. A list of requested images is provided with the image files. This list of files is then used to retrieve the same selection of images from the database directly. This, in turn, ensures reproducibility of analyses and uniquely defines each dataset. The LUPC-DC method is compared with the existing Image Prior [1], LRMA [2], Gradient Projection Method [7] and Coupled Learning Algorithm [3] for deblurring. Experimental evaluation using LUPC-DC method is conducted on various factors such as PSNR, computational time and success rate with respect to different natural images. 5 Results analysis and discussion To validate the efficiency and theoretical advantages of the LUPC-DC for image deblur of natural images with Image Prior [1], LRMA [2], Gradient Projection Method [7] and Coupled Learning Algorithm [3] performance evaluation results are presented. The parameters of the LUPC-DC method are chosen as provided in Section 4. 5.1 Case 1: Impact of PSNR To evaluate the performance of the LUPC-DC method, three experiments are conducted. The first one is designed to measure the noise ratio caused by blurred images. One of the simple ways to measure the blur introduced during image deblurring for natural images is measuring PSNR. A higher value of PSNR indicates higher natural image quality. The blur level is measured based on the size of the natural image in pixels. With deblurring to be performed for natural images, it is analogous that a significant amount of blur is appended to it. Also, the blur should be imperceptible by the Human Visual System. In the proposed method, the PSNR [20] is used to compute the low, medium, and average deblurring capacities. PSNR value is used to measure the quality of natural images. PSNR is defined by the following equation: (13)From (13), L represents the peak signal level, whereas represents the mean squared error [20], which is the pixel value of the image. MSE value is calculated using the following equation: (14)where and are the pixel intensity values of the original image and the blurred image, respectively, and n represents the size of input natural images. In image pre-processing step, the size of the input blur image is re-sized and image contrast level is improved by changing the pixel brightness values to improve its visual impact. Figs. 6a and b illustrate the input blur image 640 × 426 and pre-processed image of size 250 × 350 is used for further processing. Fig. 6Open in figure viewerPowerPoint Image pre-processing (a) Input blur image, (b) Pre-processed image used as input blur image (size 250×350 with 12 dB PSNR) In PC extraction, the input blur image is divided into a number of components such as component level 1, component level 2 and component 3. The input blurred input image is first de-correlated by which good similar patches are extracted to generate a low-rank matrix. Figs. 7a–c illustrate the PCs 1, 2 and 3, respectively, of the input blured image with 12 dB PSNR value. The features are extracted and rectified so that LUPC will provide an image with 13.99 dB PSNR. Fig. 7d shows the output image recovered by LUPC. The DCNN model is processed to jointly extract the good similar patches and deblur the PCs, which in-turn improves the PSNR to 14.55 dB. Fig. 7e shows the recovered image by the proposed LUPC-DC method. Figs. 7f–i illustrate the restored images using Image Prior [1], LRMA [2], Gradient Projection Method [7] and Coupled Learning Algorithm [3], respectively, with PSNR values. Fig. 8 shows the comparative resultant images for the sample image set. Fig. 7Open in figure viewerPowerPoint Intermediate results for sample image (a) PC 1, (b) PC 2, (c) PC 3, (d) Restored image obtained by LUPC (13.9 dB PSNR), (e) Restored image obtained by LUPC-DC (14.55 dB PSNR), (f) Recovered image using Image Prior [1] (13.62 dB PSNR), (g) Recovered Image using LRMA [2] (12.53 dB PSNR), (h) Recovered Image using Gradient Projection Method [7] (11.98 dB PSNR), (i) Recovered Image using Coupled Learning Algorithm [3] (10.27 dB PSNR) Fig. 8Open in figure viewerPowerPoint Comparative results for sample set of images (a) Blurry image, (b) Restored image by Image Prior [1], (c) Restored image by LRMA [2], (d) Restored image by Gradient Projection Method [7], (e) Restored image by Coupled Learning Algorithm [3], (f) Restored image by LUPC-DC Fig. 9 shows the measured noise level while performing deblurring based on the different natural images provided as input. The PSNR values obtained after deblurring in test natural images are comparatively larger. This result proves the better value of PSNR is achieved using the LUPC-DC method compared to Image Prior [1], LRMA [2], Gradient Projection Method [7] and Coupled Learning Algorithm [3] methods. Better PSNR values of the LUPC-DC method indicate the better quality of the resultant original natural images with an imperceptible noise level. From Fig. 9, it is also evident that the LUPC-DC method achieves improved noise level for all the natural images given as input. 100 different images extracted from UPenn Natural Image Database were used as input for measuring the noise level using the proposed LUPC-DC method and comparison analysis of Image Prior [1], LRMA [2], Gradient Projection Method [7] and Coupled Learning Algorithm [3] methods. Fig. 9Open in figure viewerPowerPoint Performance measure of PSNR Fig. 9 also shows that the noise level is the highest using LUPC-DC method because the deblurring of natural images is performed by extraction where the PCA components are initially extracted based on the linear uncorrelated model, resulting in identifying the hidden insights. This is because of the application of machine learning algorithm, called, Linearly Uncorrelated Principal Component Extraction resulting in the increased noise level when compared to of Image Prior [1] and LRMA [2], Gradient Projection Method [7] and Coupled Learning Algorithm [3]. The existing methods are unable to remove the noises in the image thus leads to reduce the performance of qualitative analysis. Besides, the high quality similar patches are separated into first i components and remaining i–n components without being explicitly programmed between the components and thus the noise is discarded in the proposed method. The noise presented in the first i component is eliminated by DCNN model. In addition, the threshold value is applied to remove the noise in the remaining component. Therefore, the PSNR of LUPC-DC method is found to be improved by 12% compared to Image Prior [1], 19% compared to LRMA, 34% compared to Gradient Projection Method [7] and 50% compared to Coupled Learning Algorithm [3]. 5.2 Case 2: Impact of computational time In the second experiment, the performance of the LUPC-DC method is evaluated in terms of computational time dealing with the natural images and compares the methods with Image Prior [1], LRMA [2] Gradient Projection Method [7] and Coupled Learning Algorithm [3]. This subsection includes the experimental results of the computational cost or time by considering various distances between the camera and objects in the scene as input. The computational time is an important factor that should be considered while performing deblurring for natural images. Computational cost or time is defined as the time consumed for deblurring the natural images and is derived by using the following equation: (15)From (15), computational time CT is arrived at on the basis of and represent the original and blur images, respectively. Here, and represent the average distortion (MSE value) computed over the original and blur images, respectively. A large amount of additive noise is a cause for the increase of computational cost or time in most of the image deblurring. This parameter is used as a basis to measure the efficiency of deblurring. Computational cost as the basis to measure deblurring efficiency in the proposed method uses and as the original image and the blurred image. Fig. 10 shows the comparison of the computational time obtained by applying the proposed and existing methods. The computational time is measured in milliseconds. As channels are used as input for an RGB natural image, computational time is measured with respect to the wavelength (i.e. in terms of a nanometre), for measuring two identical peaks (i.e. original and blur images, respectively). Fig. 10Open in figure viewerPowerPoint Performance measure of computational time From Fig. 10, it is noted that the existing methods, Image Prior [1], LRMA [2], Gradient Projection Method [7] and Coupled Learning Algorithm [3] have high computational cost. The proposed method reduces the computational cost by optimising the non-linear operation by applying the non-linear RLU, computational time is said to be reduced during deblurring with reduced noise. The noise is said to be reduced because of the most inherent PCs being detected using the PC extraction algorithm that uses blind image deblurring, based on the partial knowledge of the features, reducing the computational time. Therefore, noise is said to be improved using the LUPC-DC method, when compared to the existing methods. Lower the computational cost, lower the noise is and therefore higher the success rate. From Fig. 10, it is clear that the computational cost incurred during deblurring for natural images using LUPC-DC method is significantly lesser than that of existing state-of-the-art methods. For example, as shown in Fig. 10, the computational cost evaluated with respect to 600 nm using the proposed LUPC-DC method, Image Prior [1], LRMA [2], Gradient Projection Method [7] and Coupled Learning algorithm [3] methods are 33.32, 37.39, 42.14, 45.15 and 52.31 ms, respectively. The implementation of the blind deep convolution algorithm with the relevant additive noise in the proposed method results in low computational cost. In the LUPC-DC method, using RLU, the resultant values are stored as feature map, therefore reducing most of the computational complexity during nature image deblurring which in turn increases the success rate. In addition, DCNN has a number of layers which integrates the multiple components to the RLU reduce the time for deblurring. Moreover, deblurring is performed only after the removal of the noise and therefore reducing the computational cost in a significant manner. Thus, the LUPC-DC method achieved lesser computational cost with better success rate when compared to Image Prior and LRMA. As illustrated in Fig. 10, the proposed LUPC-DC method exhibits comparatively better analysis in terms of computational cost, considering that it outperforms the two other methods Image Prior and LRMA. The improvement in computational cost (in milliseconds) using LUPC-DC method is found to be better than 11% when compared to Image Prior,19% compared to LRMA, 25% compared to Gradient Projection Method and 29% compared to Coupled Learning Algorithm. 5.3 Case 3: Impact of success rate In the third experiment, the performance of the LUPC-DC method on UPenn Natural Image Database is assessed and compared with four methods Image Prior [1], LRMA [2], Gradient Projection Method [7] and Coupled Learning Algorithm [3]. The success rate measures the as given below and is measured in terms of percentage (%). A number of blurred images measured as blurred and the percentage of blur present in a single image. Therefore, the higher the recognition of these two factors, higher is the success rate. The success rate is mathematically evaluated (16)From (16), the success rate SR measures the percentage ratio of a number of deblurred images to the number of blurred images . Error ratio measures the ratio of a number of correctly predicted human choices to the total number of observations. Higher the error ratio, more efficient the success ratio is said to be in all the methods. Fig. 11 illustrates the measure of success rate with respect to the error ratio [1]. Comparatively, the success rate is said to be proved to be better by applying LUPC-DC method. In addition, to measure the efficiency of the LUPC-DC method, the proposed LUPC-DC method is compared with Image Prior [1], LRMA [2], Gradient Projection Method [7] and Coupled Learning Algorithm [3]. An error ratio of 0.2–2 was selected for ten different images, with image possessing different sizes. Fig. 11Open in figure viewerPowerPoint Performance measure of success rate Quantitative comparisons of success rate are shown in Fig. 11. As can be seen in the figure, the proposed LUPC-DC method has the highest success rate for almost all tested images with different error ratio. Accordingly, the average success rate of LUPC-DC method is higher than both commonly used image deblurring methods. This comparative analysis shown in the figure signifies the success of the LUPC-DC method. The improvement is due to the application of hard thresholding for denoising that initially measures MSE providing quadratic loss function and measures uncertainty involved in forecasting. This, in turn, provides correct differentiation between the estimated value and the value of the estimator, resulting in a more accurate estimate. This, in turn, reduces the noise and therefore improves the success rate of the LUPC-DC method by 25% compared to Image Prior [1], 39% compared to LRMA [2], 48% compared to Gradient Projection Method [7] and 58% Coupled Learning Algorithm [3]. 6 Conclusion In this work, LUPC-DC for image deblur of natural images is presented. The LUPC-DC method first obtains the first i component by applying the LUPC extraction. With the extracted first i component, DCNN is applied, based on the partial knowledge of the features. This is because of a large amount of blur and noise present in the first i component, therefore by removing the blur and noise, a significant amount of noise is said to be reduced, therefore improvement found in PSNR. Then, by applying a non-linear operation, the time taken for deblurring is minimised. Finally, with the remaining components, optimal Hard threshold denoising is applied. Therefore, a cooperative deblurring and denoising are said to be performed to obtain the restored natural image, therefore improving the success rate. Experimental results demonstrate that the proposed LUPC-DC method leads to reduce the computational time by 21% for image deblurring, and improve the success rate by 43% on image deblurring for natural images. It also improves the PSNR efficiency by 29% on several identification attempts over methods, namely, Image Prior [1], LRMA [2], Gradient Projection Method [7] and Coupled Learning Algorithm [3]. 7 References 1Wang H., Pan J., and Su Z. et al: 'Blind image deblurring using elastic-net based rank prior'. Comput. Vis. Image Underst., 2018, 168, pp. 157– 171 2Ren W., Cao X., and Pan J. et al: 'Image deblurring via enhanced low-rank prior', IEEE Trans. Image Process., 2016, 25, (7), pp. 3426– 3437 3Tian D., and Tao D.: 'Coupled learning for facial deblur', IEEE Trans. Image Process., 2016, 25, (2), pp. 961– 972 4Li L., Yan Y., and Fang Y. et al: 'Perceptual quality evaluation for image defocus deblurring', Signal Process., Image Commun., 2016, 48, pp. 81– 91 5Xiong J., Liu Q., and Wang Y. et al: 'A two-stage convolutional sparse prior model for image restoration', J. Vis. Commun. Image Represent., 2017, 48, pp. 268– 280 6Routray S., Ray A.K., and Mishra C.: 'Image denoising by preserving geometric components based on weighted bilateral filter and curvelet transform', Optik, 2018, 159, pp. 333– 343 7Zeng N., Zhang H., and Li Y. et al: 'Denoising and deblurring gold immunochromatographic strip images via gradient projection algorithms', Neurocomputing, 2017, 247, pp. 165– 172 8Yue T., Suo J., and Cao X. et al: 'Efficient method for high-quality removal of nonuniform blur in the wavelet domain', IEEE Trans. Circuits Syst. Video Technol., 2017, 27, (9), pp. 1869– 1881 9Zachevsky I., and Zeevi Y.Y.J.: 'Statistics of natural stochastic textures and their application in image denoising', IEEE Trans. Image Process., 2016, 25, (5), pp. 2130– 2145 10Zuo W., Ren D., and Zhang D. et al: 'Learning iteration-wise generalized shrinkage–thresholding operators for blind deconvolution', IEEE Trans. Image Process., 2016, 25, (4), pp. 1751– 1764 11Zhao W., and Lu H.: 'Medical image fusion and denoising with alternating sequential filter and adaptive fractional order total variation', IEEE Trans. Instrum. Meas., 2017, 66, (9), pp. 2283– 2294 12Wei W., Zhang L., and Tian C. et al: 'Structured sparse coding-based hyperspectral imagery denoising with intra cluster filtering', IEEE Trans. Geosci. Remote Sens., 2017, 55, (12), pp. 6860– 6876 13Qiao C., Lau R.W., and Sheng B. et al: 'Temporal coherence-based deblurring using non-uniform motion optimization', IEEE Trans. Image Process., 2017, 26, (10), pp. 4991– 5004 14Cao X., Ren W., and Zuo W. et al: 'Scene text deblurring using text-specific multiscale dictionaries', IEEE Trans. Image Process., 2015, 24, (4), pp. 1302– 1314 15Stanković I., Orović I., and Daković M. et al: 'Denoising of sparse images in impulsive disturbance environment', Multimedia Tools Appl., 2018, 77, (5), pp. 5885– 5905 16Ding Y., Cheng Y., and Cheng X. et al: 'Noise-resistant network: a deep-learning method for face recognition under noise', EURASIP J. Image Video Process., 2017, 2017, (1), p. 43 17Tofighi M., Li Y., and Monga V.: 'Blind image deblurring using row-column sparse representations', IEEE Signal Process. Lett., 2018, 25, (2), pp. 273– 277 18Wang M., Zhou S., and Yan W.: 'Blurred image restoration using knife-edge function and optimal window wiener filtering', PloS ONE, 2018, 13, (1), p. e0191833 19Tkačik G., Garrigan P., and Ratliff C. et al: 'Natural images from the birthplace of the human eye', PLoS ONE, 2011, 6, (6), p. e20409 20Das R., and Tuithung T.: ' A novel steganography method for image based on Huffman encoding'. 2012 3rd National Conf. on Emerging Trends and Applications in Computer Science (NCETACS), Shilong, India, 2012, pp. 14– 18 Citing Literature Volume13, Issue1January 2019Pages 49-56 FiguresReferencesRelatedInformation