Medical images are generally of poor contrast and they also get complex type of noise and blur. The noise also has variability from one condition to other. So it is very difficult to suggest a robust method for noise removal which works equally well for different modalities of medical images. During the denoising process of a noisy image, it is usually helpful to look at an image at different resolutions so that important information about both the image and the noise can emerge easily. If the chosen resolution is too coarse, fine details will not be visible. On the other hand, looking too closely at an object can cause surroundings to disappear, so the noise and the object cannot be distinguished easily. This is where wavelets can be useful. But unfortunately the present wavelet based techniques for medical image denoising are too particular and are useful in particular situations only. Here, it is important to mention that complex wavelet transform has not found its deserving place in many applications, and one of the major challenging tasks taken up in this work is to apply complex wavelet transform for denoising.