1 Introduction

In today’s time, almost every digital imaging application demands high-resolution images. It is mainly required for efficient processing and analysis of image details. Image resolution basically describes the details contained in an image, i.e. the higher the resolution, higher the number of pixels and more is the image detail [78]. There are a number of examples where high-resolution images are desirable like in human interpretation, surveillance, HDTV, medical imaging, satellite imaging etc. In addition to that improved resolution is also helpful in automated system perception (ASP) based applications. Therefore, improvement of pictorial information is always desirable. Super-resolution (SR) area is mainly inspired by these type of requirements. Technically, Super-resolution (SR) term is used for the class of techniques which work in up-scaling of video or images. Image SR techniques take a low-resolution (LR) image as an input and generate a corresponding high-resolution (HR) image. The terms like zooming, HR image reconstruction, digital image magnification etc. are used interchangeably for the same process [97]. In the same way terms such as up-convert, upscale, upsize also describe an increase of resolution by SR image processing [97]. Image SR schemes try to preserve the high-frequency information, geometrical regularities and smoothness of the original input image in the process of generating HR image from the source input image. Image SR has many applications in various areas e.g. high-definition television (HDTV) [], medical imaging [112], satellite-imaging [57], surveillance systems, and entertainment etc. [104, 147].

In literature, there are various methods which are available to create super-resolution (SR) from low-resolution (LR) images by maintaining the image details. Early methods of producing an SR image generally include multiple LR images as a contribution to calculate the details [9, 35, 124]. There are also multiple methods which works with single LR image and having the capability of LR to HR image conversion. In the category of multiple images based SR, there are also some multi-view based approaches [28, 29, 40, 41, 49]. The approach listed in [40] is designed for curved and multi-view surfaces. It requires the multiple images for super resolution. In [28], the method is useful in mixing the different photographs; It provides the artifact free blending and requires multiple unordered images for super resolution. The method listed in [49], is used for up sampling in real time with good GPU systems. It requires the high end GPU for geometrical up-sampling of images. Edge-Constrained Image Compositing is listed in [29]. It includes the image overlapping and stitching for Super resolution, based on multiple input images. Similarly, [41] has proposed multi-view 3D reconstruction from multiple images. On the other side, single Image based Super Resolution. Single image based methods use only one single image for super resolution and proved to be more practical in today’s time. These algorithms of SR can be categorized in different categories like Interpolation-based methods, learning based methods, Soft Computing based methods etc. which have been discussed in detail in further sections. Algorithms based on interpolations are comparatively faster in response [70, 91, 114]. In real time systems along with many practical applications, some standard interpolation based methods are being used. There are some methods of reconstruction [52, 54, 80, 90, 101, 106, 119] which applies the various smoothness priors [5, 20, 108] for SR imaging. Another approach is based on learning based methods [16, 37, 75, 129], there is a training a set of LR/HR images or blocks and detailed HR image is constructed based on learning from these pairs. Selection of training set is crucial for these methods of SR; wrong selection could lead to undesired results [21]. Recently, deep learning based methods are also becoming more popular due to their state of art performance [23, 24, 45, 59, 63, 64, 71, 103, 136, 138, 142].

1.1 Motivation and contribution

There are a number of possible approaches which could be used to address the problem of super-resolution. However, for in depth study and solution oriented approach of this problem, there is always a requirement of proper classification and systematic study of the previous approaches. Therefore, there should firstly identification of challenges related to image super resolution and then there should a systematic approach towards the solutions. In the proposed work, the main focus is concerned on Single Image Super-Resolution based solutions. In this paper, the proposed solution is threefold i.e. (a) Image Super Resolution based challenges have been identified and presented, these challenges are acting as limiting factor for the implementation of Super resolution; (b) Survey on Single Image based Super-Resolution has been presented for different type of SR methods along with their year-wise progress, (c) The comparison of different existing state of art methods of Super-Resolution is also presented in the work.

In this paper, Section 2 is presenting the basic details of Super Resolution (SR) as an inverse problem, Section 3 is presenting the identified challenges which are limiting the implementation of SR, Section 4 is giving the detailed review and survey of different methods usually used in the single image based SR including simulation based different comparisons and in the Section 5 conclusion has been presented.

2 Super resolution of images

Super-Resolution (SR) is the process of converting the low resolution image into high resolution image. In the process, the number of pixels in the input low resolution (LR) image are increased as per required scaling factor, therefore high resolution image is achieved at the output (Fig. 1).

Fig. 1
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A basic block diagram of Image Super Resolution

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The main aim of SR (Super-resolution) is to estimate a high-resolution (HR) Image from one or a set of low-resolution images. The process of reconstruction of the HR image from the input source image by adding one or more LR images is considered as an inverse problem [97]. In order to implement the super-resolution of images, proper reconstruction schemes are required. It is a very ill-posed problem since many HR images can produce the same LR image. The reconstruction of super-resolution image is centered on available prior information or rational deduction of the supposed model that builds the exaggerated image from the available LR images. Therefore, the reconstruction is reflected as the problem in the inverse route to calculate the original particulars around the geometrical symmetries of the SR image by merging one or more LR images [78]. However, due to the less prior information and ill-conditioned registration difficulties, there is always a scope to improve the quality of the reconstructed image [7]. During the literature survey, it has been comprehended that there are several methods that had been proposed to fix above-mentioned problems.

2.1 Super-resolution as an Inverse Problem

Super-resolution is an inverse problem where target information is estimated from the observed data i.e. high-resolution image from low-resolution image or images. In order to unravel the inverse problem, it requires to understand the basic down sampling model as shown in Fig. 2. Basically, Super-resolution algorithms attempt to extract the high-resolution image degraded by the limitations of the optical imaging system [7].

Fig. 2
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Model for Down Sampling

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Let low-resolution image is denoted by Yk, for k = 1,2,3…. K and a high-resolution image are denoted by X. Assume X is Linearly Spatial Invariant (LSI) and is the same for all K frames. Suppose Mk considers only simple motion parameter such as translation and rotation, Dk is a sub-sampling matrix (compression) and Nk represents the noise, then the low-resolution image can be denoted as below:

$$ {\displaystyle \begin{array}{c}{Y}_k={D}_k{M}_kX+{N}_k\\ {} where\ k=1,2,3\dots, K\end{array}} $$
(1)

With reference to the model in Fig. 2, the approach for the solution should be inverse of it i.e. It may include stages like interpolation and restoration and noise removal to get original high resolution image X in Fig. 2 [32, 35].

3 Factors limiting the implementation of SR

There are various factors which are limiting the implementation quality of SR imaging. These factors are related to many methods used to convert the low-resolution image to the high-resolution image. With reference to literature study, it has been observed that there are various types of practical challenges which are faced during the implementation of super-resolution of images and acting as limiting factors for the implementation of SR. Taking everything into account some major challenges related to super-resolution are further explained (Fig. 3):

Fig. 3
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Challenges of Super-resolution

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3.1 Registration of Multi-frame images

Image registration one of the very crucial factors for the implementation of multi-frame SR reconstruction. It includes the spatial fusion of images and it is also a well-known ill-posed problem. The problem gets more severe when low-resolution images also contain aliasing artifacts. These artifacts are more annoying than the blurring effect which may come due to interpolation of the single image. The SR performance deteriorates as the resolution of observational images decreases. The recovery of high-resolution (HR) image depends upon the image registration accuracy. There are many image registration methods which have been proposed in the literature [12, 3, 87, 102, 123, 146]. Some of registration based performance limits have been mentioned in reference [92].HR image estimation crucially depends upon the accuracy of registration of LR images [93]. In order to converge towards the practical applicability of SR, improvements are desirable in this area. Due to the challenges in registration of multiple LR images, single image based super resolution (SISR) is becoming more practical solution.

3.2 Computation

Other major limiting factor for the practical applications of Super Resolution is the high computation of a large number of unknowns, which results in extreme matrix manipulations and calculations. Practical applications always require a high speed computation in SR reconstructions, like surveillance systems which demands real-time alarms and active identifications etc. The desired Algorithms should be superior in terms of computational efficiency. One of the recent solutions is parallel computing. Parallel computing can improve the further efficiency of the system. However, its practical implementation in small power devices is a challenge. Many algorithms have been proposed until now to speed up the SR image reconstruction problem but still many are waiting to become practical on smaller devices. There is a class of algorithms which is focused upon computational efficiency known as Interpolation based approaches, however the quality of these methods is not very accurate. In reference [11] Authors have proposed a real-time based SR system which has been improved from [9, 32] in order to make SR more practical. However, despite that these algorithms are limited by precise image registration which again requires very high computation if multiple images are used. Many algorithms can also handle only simple motion models but real-world data of images/videos involves more complexity. Hardware and GPU improvements involving parallel computation can help in improving the computational efficiency but that is again limited by other cost factors of the hardware systems.

3.3 Robustness towards external factors

Robustness of SR method towards external factors is also one of the restraining factors of SR. Many of the SR techniques are affected by the motion errors, inaccurate blur models, noise, moving objects, motion blur, etc. This inaccuracy leading to a basic model error that cannot be treated as common Gaussian noise [105]. Furthermore, the basic model error will lead to visually annoying artifacts creating disturbance in applications based on image and video standards. Meanwhile, as per literature, there is not enough work has been devoted to such an important aspect of robustness towards external factors. Yet in some references [19, 14, 30, 98, 110, 128, 145, 148], authors have worked on a robust aspect of Super-resolution of images. Pham et al. [86] have proposed a bilateral filtering similar scheme for robust certainty. It has been seen that with the proper improvements in estimations of outliers or external factors, results of SR can be improved. On the other hand, for this purpose proper experimental data is required and by including that into the modeling, it can improve the robustness of real-time SR.

3.4 Fundamental limits of performance

There are always some fundamental limits of SR performance that may limit the performance or efficiency of the SR reconstruction algorithms. SR reconstruction is a complex task which involves many interdependent components. In the reference [7], authors have analyzed the limits for SR and have given analysis for Zooming factor. In addition, reference [73] has worked on fundamental limits on reconstruction-based super-resolution algorithms under local translation. Robinson et al. in reference [92] have analyzed the registration performance limit with a simple translation model and the work was further extended with analysis of factors such as motion estimation, decimation factor, number of frames, and prior information. Moreover, their understanding could lead to the better SR camera design, better understanding of model errors, zooming factors limits and number of frames required etc. Eekeren et al. [127] have given performance evaluation of super-resolution reconstruction methods on real-world data by exploring many influential factors limits empirically. Based on above mentioned literature, it is very difficult to conclude that performance limits of SR. therefore no method can be called a best SR method in terms of performance as it varies with environment and image conditions. However, based on studies, a fair benchmark can be defined for particular conditions and real-time based database may be used to give a good performance evaluation of SR methods along with their performance limits.

3.5 Compression based artifacts

Recently it has been observed that multimedia data is increasing day by day continuously and handling or storage of such a huge amount of data is in itself a big challenge. There are many limitations on transmission and storage of such data with limited resources including other cost factors. Therefore, transmission of multimedia data like images, videos are usually done in the compressed forms. It may also include the various lossy types of compression. It has been seen that due to compression quality of images goes down or may contain artifacts like blocking artifacts in jpeg based compressed images. Removal of these artifacts is very necessary if doing the super-resolution. Consequently, it makes the process more complex. In today’s time, every transmission standard contains the compression encoder /decoder. Clearly, this challenge needs to be handled suitably in every system of Super Resolution.

3.6 Other practical issues

There are various other practical issues which lead to the complexity and the quality trade-off in the SR implementations. In the practical infrastructure, there is always a probability of noise from external resources that can decrease the SNR of that channel. Therefore, it is also a practical challenge which could be seen in various transmission channels which are susceptible to noise, like wireless channels etc. Furthermore, in many applications, there are some application based local challenges which may decrease the efficiency of SR methods or might leads to errors in results.

4 Single image based super-resolution literature survey and comparison

The Previous section has listed the main challenges which affect the implementation of image Super Resolution (SR). Clearly, there is a need for work to handle these issues to get the acceptable quality of SR images. Meanwhile, there are various methods reported in the literature that have already been proposed to implement the SR. A survey of SR methods for single image based SR has been presented in this section, as single image-based methods are more realistic and practically required methods. Further with reference to Fig. 4 details of each method along with its literature survey has been discussed in subsections.

Fig. 4
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Single Image based SR techniques

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4.1 Interpolation based methods

Image interpolation focuses on creating the high resolution image from its lower resolution version of the image (Fig. 5). Image interpolation is basically a method of artificially increasing the number of pixels in an area inside an image. Image interpolation is also one of the traditional methods used in the Super Resolution. Conventional systems include the bilinear and bi-cubic interpolation which are having good real time computational simplicity. These require very limited arithmetic operations. Video interpolation or inter frame interpolation can also be achieved by these methods. Interpolation based approach is one of the fastest methods for image Super Resolution. Interpolation based SR schemes are often used when working with the real practical environment having a single LR image as input [50, 74]. Nearest neighbor (NN), bilinear (BL)and bi-cubic (BC) are the regularly used interpolation techniques [2, 6, 53]. However, these techniques are non-adaptive so they are computationally efficient but undergo with problems of aliasing, blurring etc. Even Though, these are used in numerous applications due to their simplicity of implementation. There are several adaptive non-linear schemes which have been advanced to minimalize the glitches faced by non-adaptive interpolation schemes [58, 60, 74]. In these techniques, re-sampling info is determined according to the geometrical symmetries. There is always a tradeoff among image quality, time and computational complexity, for this category of methods. In some advanced methods adaptive and interpolation based on higher order derivatives of polynomials have been suggested in literature [96, 133]. Detailed work in the field of Interpolation based SR has been presented in Table 1.

Fig. 5
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Interpolation based SR Model

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Table 1 Interpolation based SR Methods
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4.2 learning based Super-resolution

There is another approach of SR which is based upon example-based learning (Fig. 6). There are multiple methods of SR which are based on example-based learning approach as suggested in references [38, 39, 42, 48, 61, 115, 116, 121, 141]. These methods of this category are creating high-frequency details from a low-resolution image by process of example based learning. The quality of output HR images created by this method good but consumes more time due to learning process. Multiple Low-resolution images besides their corresponding high quality/high-resolution image patches are stored in the database. The SR algorithm got its training from the database of stored patches i.e. low-resolution and high-resolution image patch pairs. These techniques have certain restrictions due to the dependency on numerous factors like numbers and kind of the images present in training dataset, size of the patches etc. With a variation of these parameters the running time along with the quality of images may change i.e. there is a trade-off between these parameters. These techniques do have high time complexities so rarely used in real-time applications. Table 2 gives the survey of various method included in this category.

Fig. 6
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Learning-based SR Model

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Table 2 Learning /Example based SR Methods
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4.3 Edge directed Super-resolution

In literature, there are some methods which produces the HR images based on edge directed calculations [20, 31, 36, 56, 67, 76, 108, 109, 113, 130]. These methods are based on edge knowledge of objects in an image which is included in the calculation of HR image from LR image (Fig. 7). This category of methods are mainly an extension of the interpolation techniques. The fundamental work was done in NEDI [70] and afterwards many methods based on edge detection were published. In many extended publications it has been observed that multiple techniques are combined for edge calculations and in obtaining of HR resolution images. Furthermore, some techniques are based on the gradient profile prior (GPP) techniques [108, 109, 113]. In GPP (gradient profile prior) it is based on image data set, so HR image result relies on the accuracy of the learning process, so partially including the learning based methods. The edge knowledge in the base image helps in reproducing the HR image with sharp edges and lower artifacts. Another approaches of Super-resolution [67, 76, 130] algorithms also require to locate edges in images and work in combination of other methods. Some edge directed reconstruction models use the iteration based methods where good initialization by edge detection could lead to a reduction of iteration time and lead to good quality of HR images. Table 3 contains the major work of Edge directed SR methods that are included in this category.

Fig. 7
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Edge directed SR Model

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Table 3 Edge directed SR based Methods
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4.4 Sparsity based Super-resolution

In this class of methods, the approach is based on a sparsity based SR model (Fig. 8). It is having the sparsity based dictionaries, image details of HR are calculated from sparse properties of an image, like the model shown in Fig. 8. The image super-resolution by sparse representation has been suggested in references [1, 26, 62, 66, 77, 81, 132]. These methods include the sparse image patch prior calculations from the dictionaries. The researchers had worked on mixed estimators for l1 and l2 norms for the dictionary coefficient blocks calculations [77]. In the methods based on patch prior, it is presumed that LR and equivalent HR patches are on the same manifold in L1 space. The HR patch can be estimated from same convex combination which is present for LR patches i.e. sparse convex combinations in a dictionary. The approach is based on learning of coupled dictionary from LR-HR patch feature space. As per literature, there are various extensions for these sparse estimators [25, 88, 131]. Multiple dictionaries could also be included in spite of a single dictionary [88]. Semi coupled dictionary concept has been used for LR to HR conversion in reference [131]. This category of methods also produces the good quality of results and comparable to other methods. Table 4 represents the detailed survey of this category of methods.

Fig. 8
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Sparsity based SR Model

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Table 4 Sparsity based SR Methods
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4.5 Soft Computing (Neural and fuzzy) based Super-resolution

In recent time, it has been observed that there is a good evolution of methods for image processing based on soft computing like neural networks and fuzzy systems (Fig. 9). Fuzzy system based image processing deals with the various approaches of fuzzy systems that are useful in image processing and includes the fuzzification / defuzzzification of data. These methods also include their applications in the areas like image up-scaling, image filtering, removal of image noise, image segmentation and image interpretation [10, 15, 22, 33, 34, 51, 68, 69, 72, 82, 85, 95, 99, 100, 107, 126, 135]. Some Image upscaling related methods have been developed using the fuzzy sets which are useful for Super Resolution [8, 17, 18, 83, 89, 122]. The fuzzy based methods can be combined with interpolation based SR approaches as well as with learning based SR approaches in order to provide the improvements in SR results [18, 83]. Fuzzy rule based systems are based on imprecision which is the practical situation of every event in reality. It manages the imprecision along with the expert knowledge of the field. Fuzzy based methods are very useful for the development of learning algorithms useful in computer vision. As these are the knowledge based methods and work in a nonlinear way, so these methods deal with the artifacts in a very robust way. Table 5 lists the work of SR done with the fuzzy based methods.

Fig. 9
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Soft Computing based SR model

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Table 5 Fuzzy based SR Methods
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In the More recent literature for the Single Image based Super resolution, Neural network based Deep learning related methods has been suggested [23, 24, 45, 63, 64, 71, 103, 136, 138, 142]. In the last 10 years, the Super Resolution approaches developed on neural networks with deep convolutional Network have sharply increased. These approaches have shown good performance as compared to other SR methods. The main reason behind these developments is the advancements in hardware for fast computation with which efficiency of these methods have evolved [13, 23, 24, 45, 46, 63,66,65, 71, 103, 136, 138, 142, 143]. This category based approaches uses the neural networks which requires the training in the initial stage. That training of the network crucially decides the quality of output from these kind of methods. The performance of these systems also depends upon the quality of training database and mostly provides the state of art results with good training. The initial time to train the network might be high but once the network is trained, afterwards it produces the required results with acceptable time. The training time of network can also be further reduced with the advancement of GPU and other related hardware. Table 6 shows the main publications related to this category.

Table 6 Neural Network/ Deep Learning Based SR Methods
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4.6 Miscellaneous methods

In literature, there are also some methods which are present in addition to previous categories, like Maximum aposteriori (MAP) framework, wavelet based methods, regularization based SR approaches [44, 43, 84, 111]. These methods are similar to previous methods however the approach used in these methods is some different from defined categories. Maximum aposteriori (MAP) framework can be used for motion estimation and segmentation along with Super resolution of images [44, ]. In the presence of noise, the wavelet transform based approach can also be useful for super-resolution and it can be combined with other approaches to achieve the SR [84, 111]. Based on the combination of different approaches, some methods are also developed for the specific robust environments like web images/videos transmissions [134]. Table 7 includes miscellaneous type of methods of SR as below.

Table 7 Miscellaneous SR Methods
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4.7 Comparison of Single image based SR methods

In order to bring the study to a single platform the performance of various existing single image based SR methods from literature review have been observed. Based on above mentioned study this has been found that Interpolation based SR methods are traditional and fastest Super Resolution methods. Algorithms based on interpolations perform faster in comparison to other methods, but sometimes lacks fine details [50, 53, 96, 125, 133, 144]. Therefore, there is still scope of improvement in their performances. Edge adaptive methods basically work on reconstruction models which are edge directive. These methods use various edge directive reconstruction models to get sharp edges for SR imaging [20, 36, 67, 76, 108, 109, 130], thus are more complex as compared to interpolations based methods. Learning or training based methods use learning based approaches [38, 39, 48, 61] using a training database with a set of LR/HR images pairs. A detailed HR image is re-constructed based on Learning from these pairs. The output image quality depends upon the training dataset and wrong selection could lead to different results [36]. Learning based methods requires training of data, which is very crucial for these methods, but the process is very time consuming although giving satisfactory performances [42, 115, 116, 121, 141]. Sparsity based methods require dictionary based models [25, 26, 62, 77, 88, 131, 137] and patch based dictionary learning is there, which is similar to example learning based methods. Sparsity based SR methods are also giving good comparable results. Recently deep learning based methods derived from neural networks are also becoming more popular [23, 24, 45, 63, 64, 71, 103, 136, 138, 142]. Moreover, convolutional neural network based models are becoming more famous because of their good performance. Once the network is trained these methods perform faster than learning based methods, giving better results, but require huge amount of data for trainings and high end GPUs for processing of trainings.

4.7.1 Qualitative analysis

In order to explore the qualitative comparison of the SR methods, a qualitative analysis of the performance of high resolution images has been performed. Simulations have been performed for each class of methods, at least one recent state of the art method from each category of SR has been taken for the performance analysis. Well known qualitative matrices like PSNR, SSIM along with the computational time have been used to compare different existing SR methods for multiple scaling factors. The high resolution image results obtained from state of art SR methods for multiple scaling factors (SF) using ‘Lena’ test image shown in Fig. 10a have been presented in, Figs. 11 and 12. Fig. 11 demonstrates the super resolved images with scaling factor of ‘2’ and Fig. 12 shows the super resolution image results for the scaling factor of ‘4’.

Fig. 10
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Test Image ‘Lena’ of different sizes

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Fig. 11
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(a) –(h) High resolution Images obtained using various existing SR methods with scaling factor of ‘2’ for input ‘Lena’ image (128 × 128)

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Fig. 12
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(a) – (h) High resolution Images obtained using various existing SR methods with scaling factor of ‘4’ for input ‘Lena’ image (128 × 128)

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The comparison of visual quality of High resolution images has been shown in Fig. 11 and in Fig. 12. Tables 8, 9 and 10 demonstrates the simulations results in terms of well-known quality matrices PSNR and SSIM along with the computational time for different SR methods. Table 8 and Table 9 are for scaling factor of ‘2’ with different size of input images and in Table 10 results have been given for the scaling factor ‘4’. Results presented in Tables 8, 9 and 10 demonstrates that computational time is least in case of fundamental interpolation based methods, however the quality of the output image is average as shown in Figs. 11 (b), (c) and 12 (b), (c). Bicubic interpolation performs better in terms of PSNR and SSIM than the bilinear interpolation at different scaling factors of ‘2’ and ‘4’. An edge oriented method proposed in NEDI [70] switches among bilinear and covariance based adaptive interpolation for the reconstruction of high resolution image that gives good visual quality for both scaling factors as shown in Figs. 11 (d) and 12(d). With reference to the Tables 8, 9 and 10, the computational complexity and time for this method has been increased with moderate PSNR with better visual quality than the interpolation based methods at different scaling factors of ‘2’ and ‘4’. In the next method [137] (ScSR), it is a Sparsity based method which works on dictionary based usage. The performance time of ScSR may vary depending upon the level of dictionary used. In simulations results as given Tables 8, 9 and 10, it has been observed that ScSR [137] has given good PSNR and SSIM value, however at the same time it takes the higher computational time. The visual results shown in Figs. 11e and 12e for scaling factor of ‘2’ and ‘4’ are also good. In case of self-example based method [121], it is a learning based method which uses the anchored neighborhood regression for the LR to HR mapping. This method has given the good results in terms of PSNR and SSIM but computational time is higher than all other considered methods. The visual quality of method shown in Figs. 11f and 12f is sharper than ScSR [137].SRCNN [24] is based on convolutional neural network, the performance of the method depends upon the training of neural network. VDSR [63] is based on very deep learning where residual learning based network has been used and its performance is faster than SRCNN. SRCNN and VDSR have given the good results in terms of visual quality as given Figs. 11(g-h) and 12(g-h). In Tables 8, 9 and 10, both PSNR and SSIM values for SRCNN and VDSR are comparable to the other state of art methods like ScSR and self-learning based methods. However, these methods required to pre-train their network in order to get good results. The residual training concept was used in VDSR which was not used in SRCNN and has taken lesser computational time than SRCNN. Neural network based method specially based on Deep neural networks, take much time to train the network i.e. from hours to days, but once network model is trained, in future that network may result in good performance for SR. It is to mention that the performance of all these methods may vary depending upon the hardware and other parameters used for the execution of these methods, however the comparative performance almost remains same and can be generalized. In order to generalize and to summarize the comparison based on the study of literature and analysis, a comparison between different SR techniques has been presented in tabular form in Table 11.

Table 8 Comparison of different SR Methods using PSNR, SSIM indices along with the computational time for Scaling factor of ‘2’ for input ‘Lena’ image (128 × 128)
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Table 9 Comparison of different SR Methods using PSNR, SSIM indices along with the computational time for Scaling factor of ‘2’ for input ‘Lena’ image (256 x 256)
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Table 10 Comparison of different SR Methods using PSNR, SSIM indices along with the computational time for Scaling factor of ‘4’ for input ‘Lena’ image (128 x 128)
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Table 11 Comparison of single image based super resolution (SISR) Methods
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4.8 Survey Comparison

Super resolution is a very important and classic problem in the image process. It is still an active area of research and many researchers have given their valuable contribution in this area. There are some other survey papers published in the literature [4, 27, 47, 55, 79, 94] which have discussed the various Super Resolution methods. The brief comparative details of year wise surveys are presented in Table 12.

Table 12 Year wise surveys comparison on Super Resolution
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In the proposed survey, an effort has been made to cover all types of the single image based SR techniques. In the presented work firstly challenges of Super Resolution have been stated and then as possible solutions based on different techniques from literature have been presented. In comparison to previous surveys, identified challenges of SR methods along with their year wise progress in different techniques has been explained. In the presented work, each method’s literature review has been included. In order to summarize the proposed study, Figs. 13 and 14 represents the diagrammatic approach of complete work. In Fig. 13, Distribution of Research Papers selected by publication year has been presented. Fig. 14 represents the distribution of Research Papers selected as per methods for Single image based Super-resolution.

Fig. 13
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Distribution of Research Papers selected by publication year

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Fig. 14
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Distribution of Research Papers selected as per methods for Single image based SR

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5 Conclusions

In the proposed work various issues related to the implementation of Super Resolution (SR) along with Single Image based Super Resolution implementation methods published in literature have been presented. Basically, super-resolution is an inverse problem, considerably there are various challenges to achieve it. It is one of the classic problems where various researchers have given their contribution by proposing various methods in order to implement the Super-resolution. Details of various techniques for Single image based Super resolution from beginning to current methods have been discussed in the paper. The comparison based on simulations is also presented for various state of art methods. However, depending upon the particular application, suitable SR technique could be selected. Moreover, in today’s time, everything is digital and need for data transportation is increasing which may also contain multimedia data i.e. images and videos. Therefore, many times images are compressed or converted to low resolution with various standards and clearly there is always a need for the reverse process of compression like Super-resolution. As a conclusive remark, it could be stated that there is a basic need of low computational fast SR methods which could be implemented for real time applications with acceptable quality of resultant images.