A vehicles license plate tracking with sparse representation. A digital image processing method is based on sparse representation to identify the blurred images from the license plate for fast moving vehicles. The detection of fast moving vehicle is an important part in Intelligent Transportation System. A new method for detecting vehicles, which violate rules in real time traffic scenario. The length of the motion kernel with Radon transform in Fourier domain which handles large motion blur even when the license plate is unrecognizable by human. It is used to identify the vehicles which crosses the speed limit and also it is useful in hit and run accidents. Experiment results show that this method can improve the efficiency of the moving vehicles license plate detection without blur greatly.