Light propagating through atmosphere will be distorted as a result of the random changing index of refraction along the light Path. This distortion lowers the optics system performance. Wavefront distortion can be compensated and corrected by adaptive optics systems. For real time compensation, systems must respond fast to the changing wavefront information. Three basic reconstruction schems are studied and fast algorithm is proposed using the block and sparse structure of the transformation matrix. Different wavefront reconstructions show that the algorithm is very effective.