An efficient GEM model for image inpainting using a new directional sparse representation: Discrete Shearlet Transform

In this paper, we present a novel Expectation Maximization (EM) algorithm for automatic color image inpainting using a new discrete multi scale directional sparse representation called the Discrete Shearlet Transform (DST). It is now acknowledged that the traditional wavelets are not very effective when dealing the multi dimensional signals having distributed discontinuities such as edges. To achieve a more efficient representation one has to use basis elements with much higher directional sensitivity. Using a Shearlet Transform combines the power of multi scale methods with a unique ability to capture the geometry of multidimensional data and is optimally efficient in representing images with edges. The inpainting can be viewed as an interpolation or estimation problem with missing data. Towards this goal, we propose the idea of using Expectation Maximization (EM) algorithm in a Bayesian Framework, which is used to recover the missing samples using a sparse representation-Discrete Shearlet Transform (DST). We first introduce an easy and efficient sparse representation-Discrete Shearlet Transform (DST) based iterative algorithm for image inpainting. And then, we derive its convergence properties. We can demonstrate that this algorithm based on a new sparse representation-Discrete Shearlet Transform is very competitive in image inpainting applications both in terms of performance and computational efficiency.