Maximally Smooth Image Recovery in Transform Coding

This paper considers the reconstruction of images from partial coefficients in block transform coders and its application for packet loss recovery in image transmission over ATM networks. The proposed algorithm makes use of the smoothness property of common image signals and produces a maximally smooth image among all those with the same coefficients and boundary conditions. It recovers each damaged block by minimizing the intersample variation within the block and across the block boundary. The optimal solution is achievable through two linear transformations, where the transform matrices depend on the loss pattern and can be calculated in advance. The reconstruction of contiguously damaged blocks is accomplished iteratively, using the previous solution as the boundary conditions in each new step. This technique is applicable to any unitary block-transform and is very effective for recovering the DC and low-frequency coefficients. When applied to still image coders using the discrete cosine transform (DCT), high quality images have been reconstructed in the absence of many DC and low-frequency coefficients over spatially adjacent blocks. When the damaged blocks are made isolated by the use of block interleaving, satisfactory results have been obtained even when all the coefficients are missing.