In this paper we present a new non-linear image recovery algorithm which is based on the theory of projections onto convex sets (POCS) to reconstruct compressed images. We introduce a new family of convex smoothness constraint sets. These sets are based on the concept of the line process which models explicitly the edge structure of images and thus can eliminate both ringing and blocking coding artifacts. We also introduce a divide-and-conquer (DAC) strategy to compute the projections onto the new smoothness sets efficiently. Finally, we present experiments that demonstrate the effectiveness of the new smoothness constraint sets.
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