# Modelling and Analysis of Hybrid Transformation for Lossless Big Medical Image Compression
###### Abstract  
Due to rapidly developing technology and new research innovations, privacy and data preservation are paramount, especially in the healthcare industry. At the same time, the storage of large volumes of data in medical records should be minimized. Recently, several types of research on lossless medically significant data compression and various steganography methods have been conducted. This research develops a hybrid approach with advanced steganography, wavelet transform (WT), and lossless compression to ensure privacy and storage. This research focuses on preserving patient data through enhanced security and optimized storage of large data images that allow a pharmacologist to store twice as much information in the same storage space in an extensive data repository. Safe storage, fast image service, and minimum computing power are the main objectives of this research. This work uses a fast and smooth knight tour (KT) algorithm to embed patient data into medical images and a discrete WT (DWT) to protect shield images. In addition, lossless packet compression is used to minimize memory footprints and maximize memory efficiency. JPEG formats' compression ratio percentages are slightly higher than those of PNG formats. When image size increases, that is, for high-resolution images, the compression ratio lies between 7% and 7.5%, and the compression percentage lies between 30% and 37%. The proposed model increases the expected compression ratio and percentage compared to other models. The average compression ratio lies between 7.8% and 8.6%, and the expected compression ratio lies between 35% and 60%. Compared to state-of-the-art methods, this research results in greater data security without compromising image quality. Reducing images makes them easier to process and allows many images to be saved in archives. big data; data security; knight tour; steganography; wavelet transform; lossless compression 2023103333310333103331033310331033103310331031033103  
performs the embedding, and the binary information is embedded in the LSB position of the medical big data image pixels placed in the KT path. To increase security, the discrete wavelet transform (DWT) is applied to the cover image to make it unreadable, and lossless wavelet compression is used to efficiently store the transformed image in an extensive medical data repository. This hybrid approach ensures the security of patient information and the efficient storage of information in a medical database using as little storage space as possible. Initial attempts to implement communications, photo archiving systems and teleraliology applications have encountered significant obstacles. Large picture files present problems for both transmission and storage due to the high cost of the equipment required to manage them. Lossless compression techniques only accomplish 2:1 to 3:1 reductions for medical photos by using redundancy within an image to transfer image information more effectively while permitting flawless reconstruction. Images can be reduced by arbitrarily huge ratios using irreversible or \"lossy\" processes, but the original pictures are not fully replicated. However, the reproduction quality could be sufficient to prevent visible picture deterioration and diminished diagnostic usefulness. This paper examines wavelet compression in a new light. We compare the method to the famous Joint Photographic Experts Group (JPEG) approach. We review methods for measuring compression algorithms' effectiveness and look at new developments in wavelet compression. The motivations behind this research work, along with the significant contributions respecting processes, are as follows:  
* Compressing the image--Apply wavelet analysis to separate and approximate the image information based on the sub-images and sub-signals. * Pixel approximation for compression--Apply the images' horizontal, vertical, and diagonal features and approximate the sub-signals for better pixel approximation.