## 1 Introduction  
The statistical analysis of images is restricted due to the depth of focus while sensing different images. The main problem is that the focus is not equally concentrated on objects which exist in an image [1]. A feasible solution to overcome the above problem is composite imaging. Composite imaging is one of the techniques used in Multi-focus Image Fusion (MIF), which combines multiple numbers of images with the concentration of different focus levels related to the same scene [2]. The spatial and transform domain methods are applicable in MIF [3]. Transform base methods are also called multiresolution algorithms. The main principle of transform domain algorithms is to maintain perceptual vision with accurate information in a multiresolution representation. Various studies indicate that several multiresolution methods have been developed, such as discrete wavelet transform (DWT), stationary wavelet transform (SWT), double density discrete wavelet transform (DDDWT), etc. [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. Lack of spatial orientation selectivity is the main issue with pyramid-based approaches, which causes blocking effects in the fused image. These pitfalls can be avoided by using DWT. However, DWT has issues with directionality, shift invariance, and aliasing. Primary factors influencing the quality of fused images are shift-invariance and directional selectivity. Traditional wavelet-based fusion techniques generate ringing artifacts into the fused images, which restricts the use of DWT for image fusion. The DTCWT [16; 17], one of the most accurate ones, overcomes the DWT's limitations in shift invariance and directional sensitivity. The directional selectivity and near-shift invariance of DTCWT allow it to properly represent features in the fused image. Developing filters in DTCWT is a little more challenging since bi-orthogonal, and phase limitations must be met. The qshift DTCWT is a technique for simplifying filter design in DTCWT that produces superior fusion outcomes. The qshift DTCWT has succeeded as a multi-resolution transform intended for image fusion because it can capture directional and shift invariant characteristics. The objective of the proposed approach is to create a high-quality fused image that is smoother, has improved visuality, and is free of distortions and noise. Users can easily perceive details in these images. The majority of MIF algorithms have an inadequate spatial resolution, which causes blurring. On fused images, the qshiftDTCWT approach has a significant impact. This technique effectively enhances the resolution of fused images and yields high-quality results. The LP [18; 19; 20], and MPCA [19] methods also do better in terms of lowering additive noise, reducing distortion, and maintaining edges and other crucial values such as image sectors with higher contrast. As shown by the visual, and quantitative results, the proposed method gets rid of these problems and produces better quality measurement results. Furthermore, the proposed formulation performs well in MIF. Several approaches for MIF were proposed in the past decades. For example, in the Nonsubsampled Contourlet Transform (NST) domain, [PERSON] et al. proposed an effective image fusion model using an enhanced adaptive pulse coupled neural network (PCNN). The proposed methodology has utilized the subbands of the source images obtained by the NST algorithm in the image fusion process. The adaptive linking strength is estimated using a new fractal dimension-based focus measure FDFM algorithm [21]. A review of region-based fusion techniques was presented by [PERSON] et al. based on the classification of region-based fusion approaches. For the comparison of the mentioned existing approaches, fusion objective assessment indicators are emphasized [22]. [PERSON], and colleagues proposed a MIF approach for improving imaging systems. The cascade forest was incorporated into MIF to estimate the influence of fusion rules [23]. [PERSON] et al.