Image inpainting using sparse reconstruction methods with applications to the processing of dislocations in digital holography

Abstract: This report is a master thesis, written by an engineering physics and electrical engineering student at Luleå University of Technology.The desires of this project was to remove dislocations from wrapped phase maps using sparse reconstructive methods. Dislocations is an error that can appear in phase maps due to improper filtering or inadequate sampling. Dislocations makes it impossible to correctly unwrap the phasemap.The report contains a mathematical description of a sparse reconstructive method. The sparse reconstructive method is based on KSVDbox which was created by R. Rubinstein and is free for download and use. The KSVDbox is a MATLAB implementation of a dictionary learning algorithm called K-SVD with Orthogonal Matching Pursuit and a sparse reconstructive algorithm. A guide for adapting the toolbox for inpainting is included, with a couple of examples on natural images which supports the suggested adaptation. For experimental purposes a set of simulated wrapped phase maps with and without disloca-tions were created. These simulated phase maps are based on work by P. Picart. The MATLAB implementation that was used to generate these test images can be found in the appendix of this report such that they can easily be generated by anyone who has the interest to do so. Finally the report leads to an outline of five different experiments that was designed to test the KSVDbox for the processing of dislocations. Each one of these experiments uses a different dictionary. These experiments are due to inpainting with, 1. A dictionary based on Discrete Cosine Transform. 2. An adaptive dictionary, where the dictionary learning algorithm has been shown what thearea in the phase map that was damaged by dislocations should look like. 3. An adaptive dictionary, where the dictionary learning algorithm has been allowed to trainon the phase map that with damages. This is done such that areas with dislocations areignored. 4. An adaptive dictionary, where training is done on a separate image that has been designedto contain general phase patterns. 5. An adaptive dictionary, that results from concatenating the dictionaries used in experiment 3 and 4. The first three experiments are complimented with experiments done on a natural image for comparison purposes.The results show that sparse reconstructive methods, when using the scheme used in this work, is unsuitable for processing of dislocations in phase maps. This is most likely because the reconstructive method has difficulties in acquiring a high contrast reconstruction and there is nothing in the algorithm that causes the inpainting from any direction to match with the inpainting from other directions.