## 1 Introduction
Numerous imaging fusion approaches are now being used in various applications, including security, remote sensing, machine vision, and medical imaging, thanks to recent technological breakthroughs. It is still necessary to investigate a variety of difficulties related to image fusion, specifically in biomedical image fusion. Additionally, a suitable, accurate and consistent fusion technique is needed for the various image types for diverse domains, which should be simple to understand to get better results. In addition, misregistration is a significant problem discovered when fusing images. Hence image fusion solutions must be resilient against unpredictable acquisition conditions or reasonable computing time in real-time systems. The critical idea of the proposed method is to investigate the suitability of the hybrid wavelet transforms using texture energy rules for a wide range of standard test images, including biomedical images. Further, it is well known that in the case of wavelet transform-based methods, the image is transformed into another space (using a transformation function) so that the texture is more easily distinguishable in the new space. The directional selectivity and shift invariance of the fused image are two factors that significantly impact its quality. As a result of their weak directionality and shift invariance, conventional wavelet-based transforms, on the other hand, result in ringing distortions and aberrations. In order to address the shortcomings of the conventional wavelet-based fusion technique and maintain the directional and shift invariance qualities, the hybrid wavelet fusion algorithm uses _DTCWT_ in combination with _SWT_. High-frequency components in this extraction are thought to execute the absolute-maximum fusion rule, while low-frequency components are thought to implement _TEM_. The absolute-maximum fusion rule is applied to the specific sub-bands. The accuracy of the output image after the fusion process is considerably increased by the texture energy rules classification of the image. The proposed method aims to eliminate distortion for a better-quality fused image. Most multi-focus image fusion (_MIF_) algorithms suffer from blurring because of low spatial resolution. The _SWT_ and _DTCWT_ used with the _TEM_ method considerably affect composite images. The proposed method successfully improves the quality of fused images by increasing their resolution, decreasing additive noise, minimizing distortion, and preserving edge detail and other important values such as the contrast in high-contrast regions of the image. The key contributions of the proposed work are as follows:  
1. Multi-focus images are fused using a hybrid technique, i.e., Hybrid Wavelet with _TEM_;
2. In the case of transform wavelet-based methods, the image is transformed into another space (using a transformation function) so that the texture is more easily distinguishable in the new space;
3. The procedure plays a dominating role in the fusion of several source images to create a new image with enhanced quality, directionality, shift invariance, visual quality, and information retention over the source images;
4. Using _TEM_ Laws, various image characteristics are extracted. Using these attributes for fusion results in a fused image with much information;
5. A process of analysing has been done both quantitatively and qualitatively;
6. Feature extraction is more efficient than traditional methodologies. The continuing parts are arranged as ensues: The proposed fusion concept is discussed in Section 2. Section 3 outlines the experimental results. Section 4 discussed qualitative comparison. Section 5 gives the conclusions.