Denoising using Matrix Completion by Hima

Video denoising has been an important task in many multimedia and computer vision applications. Recent developments in the matrix completion theory and emergence of new numerical methods which can efficiently solve the matrix completion problem have paved the way for exploration of new techniques for some classical image processing tasks. Recent literature shows that many computer vision and image processing problems can be solved by using the matrix completion theory. This thesis explores the application of matrix completion in video denoising. A state-of-the-art video denoising algorithm in which the denoising task is modeled as a matrix completion problem is chosen for detailed study. The contribution of this thesis lies in both providing extensive analysis to bridge the gap in existing literature on matrix completion frame work for video denoising and also in proposing some novel techniques to improve the performance of the chosen denoising algorithm. The chosen algorithm is implemented for thorough analysis. Experiments and discussions are presented to enable better understanding of the problem. Instability shown by the algorithm at some parameter values in a particular case of low levels of pure Gaussian noise is identified. Artifacts introduced in such cases are analyzed. A novel way of grouping structurally-relevant patches is proposed to improve the algorithm. Experiments show that this technique is useful, especially in videos containing high amounts of motion. Based on the observation that matrix completion is not suitable for denoising patches containing relatively low amount of image details, a framework is designed to separate patches corresponding to low structured regions from a noisy image. Experiments are conducted by not subjecting such patches to matrix completion, i instead denoising such patches in a different way. The resulting improvement in performance suggests that denoising low structured patches does not require a complex method like matrix completion and in fact it is counter-productive to subject such patches to matrix completion. These results also indicate the inherent limitation of matrix completion to deal with cases in which noise dominates the structural properties of an image. A novel method for introducing priorities to the ranked patches in matrix completion is also presented. Results showed that this method yields improved performance in general. It is observed that the artifacts in presence of low levels of pure Gaussian noise appear differently after introducing priorities to the patches and the artifacts occur at a wider range of parameter values. Results and discussion suggesting future ways to explore this problem are also presented.