The widely used standard for medical image storage and transmission is named as Digital Imaging and Communication in Medicine (DICOM). In every field of medicine including diagnosis, treatment, and research, medical images that are obtained as the outputs of the techniques such as the Computerized Tomography (CT), magnetic resonance (MR), digital subtraction angiography (DSA) and Ultrasonography (US) are saved as DICOM format. Network sharing of these larger sized radiology images require large bandwidth. Hence before transferring, compression of such larger image files is necessary for easy and faster communication even with lower bandwidth. Huge amount of data either in multidimensional or multiresolution form is been created as a result of medical information. This makes the following steps like retrieval, efficient storage, management, and transmission of these data a complex process. This complexity could be reduced by compressing the medical data without any loss. Many methods have been proposed so far for compression of the large DICOM images, however with some limitations. Thus, specific methods to overcome the limitations like reducing the noise of MSE error signal and improving the PSNR value results in the medical images are to be proposed for the study. One such method is referred as Hybrid Weibull Probability Density Function based Continuous Wavelet based controulet transform (WPDF-CWBCT) that helps for compression of medical images without any data loss and also for improving the PSNR and reducing the MSE of the signal. The directional filter banks are being applied by initializing using the wavelet transform such that the image coding scheme is maintained based on the proposed transform. WPDF-CWBCT also uses a new set partitioning in hierarchical trees by employing a sorting method (SPIHT) algorithm that provided an embedded code. In this method, the diagnostics capabilities are not compromised to ensure the better performance of image compression is also been justified by the combination of wavelet based controulet transform and SPIHT. The performance evaluation of different DICOM and medical images is possible by using parameters like PSNR, MSE and image compression quality measures.