X-rays and other medical images are distorted because of the limitations of the Imaging system. The other source from where the distortions get in are the transmission channels. The distortions are generally noise and blur. Unless and until the medical images are free of noise and blur they cannot be used by medical professionals to the full extent for diagnosis purpose. Therefore these images must be restored properly before they are used for diagnosis purpose. There are different restoration techniques out of which one is Blind Image Deconvolution. X-ray images restored with this technique have ringing effect in them. Using edgetaper (matlab function) prior to Blind Image Deconvolution reduces the ringing effect to an extent. This paper presents Blind Deconvolution algorithm with weights which gives lesser ringing effect in X-ray images when they are restored.