On Missing Data Prediction using Sparse Signal Models: A Comparison of Atomic Decompositions with Iterated Denoising

In this paper we consider the recovery of missing regions in images and we compare the performance of two recent prediction algorithms that utilize sparse recovery. The first algorithm is based on recent work that tries to find sparse atomic decompositions (AD) using l1-norm regularization, 3, 16 while the second algorithm employs iterated denoising (ID). 8 Experimental results indicate that ID generally outperforms the l1 based technique and we investigate the reasons for the often substantial performance difference. We discuss many issues that effect the robustness of the l1 based technique and in particular, we point to inherent problems in the missing data prediction setting that challenge the underlying sparse atomic decomposition assumptions at their core. Inspired by what ID does right, we provide techniques that are expected to improve the performance of sparse atomic decomposition motivated algorithms and we establish connections with ID.