Recently, a large number of researchers start to research the utilization of the wavelet transformation. In such a maneuver, they endeavor to handle the SR problem and to extract the complete details which are usually dropped or degraded through the procedure of the image acquisition. This is motivated by the fact that the wavelet transformation offers a strong and effective multi-scale representation of the image for retrieving the high-frequency details (Nguyen & Milanfar, 2000). This method commonly treats the LR images as low-pass filter of the unidentified HR image. The goal of this method is to approximate the scale subband coefficients, which it is accompanied by employing the inverse wavelet transformation to create the HR image.Nguyen and Milanfar (Nguyen & Milanfar, 2000) use wavelet interpolation accompanied by restoration technique for SR. They initially compute the wavelet coefficients of LR images. After that, they interpolate them for blurred values at the HR grid points. Through deconvolving, an estimation of HR image is achievable if the interpolated values are well-known blurring. El-Khamy and et al. (El-Khamy, Hadhoud, Dessouky, Salam, & El-Samie, 2005) execute the registration of multiple LR images in the wavelet domain. Wavelet coefficients are denoised and merged after registration by utilizing a regularization method. Interpolation strategies are used to obtain HR wavelet coefficients. Lastly, an inverse wavelet transform is executed to obtain the HR image in the spatial domain. Chappalli and Bose (Chappalli & Bose, 2005) additionally applies very soft thresholding methods to eliminate the noise from the wavelet coefficients and build up a real-time denoising for SR reconstruction strategy. Ji and Fermuller (Ji & Fermüller, 2006, 2009) offer a powerful wavelet SR method to tackle the mistake incurred in both the registration computation and the blurring detection computation. In this way, they break down the wavelet coefficients directly onto two channels. Finally, these coefficients seem to be up-sampled, filtered, and merged to obtain the simulated image. The SR image is gathered using iterative back projection technique with effective regularization conditions at each iteration to eliminate the noise. Li (Xin Li, 2007) suggests image resolution improvement by extrapolating high-band wavelet coefficients. Anbarjafari and Demirel (Anbarjafari & Demirel, 2010) recommend an exciting new SR technique depending on interpolation of the high-frequency subband images acquired by DWT and the input LR images. The suggested technique takes advantage of DWT to decompose an image into several subband images. Then, the high-frequency subband images and the input LR images are generally interpolated accompanied by merging them to obtain a new HR image using inverse DWT.
Zadeh and Akbari (Zadeh & Akbari, 2012) offer a multi-wavelet and cycle-spinning based on improvement approach to increase image resolution. The proposed approach produces a HR image using the input LR images and an inverse multi-wavelet transform. Panda and Jena (Panda & Jena, 2016) have taken into account the wavelet transformation to regenerate the enhanced image. Moreover, the genetic algorithm can be used to smooth the noise and obtain an ideal SR image.A bicubic interpolation approach is generally executed in the same manner of the bilinear interpolation approach by taking into consideration the nearest 4×4 neighbors of known pixels. Since, they are at different distances from the unidentified pixel so that this approach can relatively obtain a clear image quality. However, it requires a greater amount of computation. Therefore, this approach generates visibly sharper images in comparison to the previous two approaches. It perhaps gets the optimal mixture of processing time and output quality (Xin Li & Orchard, 2001). Additionally, this approach can be widely used in a large number of image processing applications such as Adobe Photoshop, Adobe After Effects, Avid and Macromedia Final Cut Pro etc. A New Edge Directed Interpolation (NEDI) (Xin Li & Orchard, 2001) is another approach. The interpolated pixels are estimated from the local covariance parameters of the LR images depending on the geometric duality among the LR and HR covariance.
An Edge Guided Interpolation (EGI) approach (L. Zhang & Wu, 2006) splits the neighbor of every pixel to make a couple observation subsets through the orthogonal directions and estimate the lacking pixel. This approach merges both of the estimated values into the powerful estimation by applying linear-minimum mean square error estimation. A gradient-based adaptive interpolation (Chu, Liu, Qiao, Wang, & Li, 2008) takes into consideration the distance among the interpolated pixel and the nearby respected pixel. The results of this suggested technique increases and enhances the quality of recovered images. Furthermore, it is a powerful technique to detect the registration mistake and needs a low-computational cost.
A cubic spline approach (X. Zhang & Liu, 2010) meets a piecewise continuing curve and moving through lots of points. The fundamental job of the cubic spline interpolation approach is to compute weights that are used to interpolate the information. The registration, interpolation, and restoration steps in the SR approach can be executed to accomplish the HR image that comes from a series of LR images through an Iterative Back Projection (IBP) approach (Irani & Peleg, 1991). In IBP approach, the HR image is approximated by reducing the error among the simulated and observed LR images. This approach is extremely easy to understand and very simple. However, it is not generally going to give an unique result because of the ill-posed trouble. An additional simply implemented SR approach is the Projection Onto Convex Set (POCS) approach that has been developed by Stark and Oskoui (Stark & Oskoui, 1989). In POCS approach, a set of restrictions are described to limit the space of HR image. The restriction sets are curved and facilitated the particular attractive of SR image features such as positivity, smoothness, bounded energy, and dependability. The intersection coming from all these sets represents the area of the allowable solution. As a result, this problem is minimized to locating the intersection of the restriction sets. The projecting operators are decided for every convex restriction set to get the solution. This operator reflects the primary estimation of the HR image against the relevant restriction set. Repetitively executing this method, a great solution is acquired at the area of intersection of the k convex restriction sets. This approach actually does not integrates any observation noise.
In order to enhance the quality of an image, various methods are suggested to improve the interpolation based approaches such as:
Ur and Gross (Ur & Gross, 1992) execute a non-uniform interpolation of a couple of spatially shifted LR images. They use the generalized multi-channel sampling theorem. The benefit of this method is the low-computational cost, which it is actually ideal for real-time applications. However, the ideality of the whole rebuilding process is not assured, because of the interpolation mistakes are not considered. Komatsu et al. (Komatsu, Aizawa, Igarashi, & Saito, 1993) show a new scheme to obtain a better resolution image. They apply the Landweber algorithm at multiple images concurrently with multiple cameras. In addition, they make use of the block-matching approach to measure comparative shifts. If the cameras currently have the same aperture, it enforces serious restrictions both in their agreement and in the configuration of the scene. Bose and Ahuja (N. K. Bose & Ahuja, 2006) make use of the moving least square (MLS) approach to approximate the intensity value at each pixel position of the HR image.