Edge preserved enhancement is of great interest in medical images. Noise present in medical images affects the quality, contrast resolution, and most importantly, texture information and can make post-processing difficult also. An enhancement approach using an adaptive fusion algorithm is proposed which utilizes the features of shearlet transform (ST) and total variation (TV) approach. In the proposed method, three different denoised images processed with TV method, shearlet denoising, and edge information recovered from the remnant of the TV method and processed with the ST are fused adaptively. The result of enhanced images processed with the proposed method helps to improve the visibility and detectability of medical images. For the proposed method, different weights are evaluated from the different variance maps of individual denoised image and the edge extracted information from the remnant of the TV approach. The performance of the proposed method is evaluated by conducting various experiments on both the standard images and different medical images such as computed tomography, magnetic resonance, and ultrasound. Experiments show that the proposed method provides an improvement not only in noise reduction but also in the preservation of more edges and image details as compared to the others.