A large number of algorithms based on partial differential equations (PDE) have recently been proposed to tackle the problems of noise removal, image enhancement and image restoration in real images. Starting with a noisy original image, the algorithms remove noise and enhance the original image by iterating the image using various schemes that are controlled by mean curvature, min/max flow, etc. We first present a variational approach such that during image restoration, edges detected in the original image are being preserved, and then we compare in a second part, the mathematical foundation of this method with respect to some of the well known methods recently proposed in the literature within the class of PDE based algorithms. The performance of our approach will be carefully examined and compared to some of the most recent algorithms proposed in the literature within the class of PDE based algorithms. Experimental results on synthetic and real images will illustrate the capabilities of all the studied approaches.