This paper presents a new combined local and global transform domain-based feedback image enhancement algorithm for medical diagnosis, treatment, and clinical research. The basic idea in using local alfa-rooting method is to apply it to different disjoint blocks with different sizes. The block size and alfa-rooting parameters driven through optimization using the Agaian's cost function (image enhancement non-reference quality measure). The presented new approach allows enhancing MRI and CT images with uneven lighting and brightness gradient by preserving the local image features/details. Extensive computer simulations (CS) on real medical images are offered to gage the presented method. CS shows that our method improves the contrast and enhances the details of the medical images effectively compared with the current state-of-art methods.