Second-order derivative-based smoothness measure for error concealment in DCT-based codecs

We study the recovery of lost or erroneous transform coefficients in image and video communication systems employing discrete cosine transform (DCT)-based codecs. Previously, we have developed a technique that exploits the smoothness property of image signals and recovers the damaged blocks by maximizing a smoothness measure. There, the first-order derivative was used as the smoothness measure, which can lead to the blurring of sharp edges. In order to alleviate this problem, we propose to use second-order derivatives as the smoothness measure. Our simulation results show that a weighted combination of the quadratic variation and the Laplacian operator can significantly reduce the blurring across the edges while enforcing smoothness along the edges.