I want to do histogram equalization in L channel of image and denoising in a or b channel of Lab color space and then use k-means to segment the tumor from MRI images.
Adaptive denosing methods out performs when compared to the conventional denoising methods. The strength of the adaptive methods is it preserves the edge details. Check whether the noise is mottle or electronic noise or computational noise and decide the adaptive methods. Not all methods are applicable in all these three types of noise.
From the question it is not clear abut what type of noise your image has from the above three types.