IMAGE AND VIDEO ENHANCEMENT USING SPARSE CODING, BELIEF PROPAGATION AND MATRIX COMPLETION

Super resolution as an exciting application in image processing was studied widely in the literature. This dissertation presents new approaches to video super resolution, based on sparse coding and belief propagation. First, find candidate match pixels on multiple frames using sparse coding and belief propagation. Second, incorporate information from these candidate pixels with weights computed using the Nonlocal-Means (NLM) method in the first approach or using SCoBeP method in the second approach. The effectiveness of the proposed methods is demonstrated for both synthetic and real video sequences in the experiment section. In addition, the experimental results show that my models are naturally robust in handling super resolution on video sequences affected by scene motions and/or small camera motions. Moreover, in this dissertation, I describe a denoising method using low-rank matrix completion. In the proposed denoising approach, I present a patch-based video denoising algorithm by grouping similar patches and then formulating the problem of removing noise using a decomposition approach for low-rank matrix completion. Experiments show that the proposed approach robustly removes mixed noise such as impulsive noise, Poisson noise, and Gaussian noise from any natural noisy video. Moreover, my approach outperforms state-of-the-art denoising techniques such as VBM3D and 3DWTF in terms of both time and quality. My technique also achieves significant improvement over time against other matrix completion methods

A Nonconvex Projection Method for Robust PCA

Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and apply an alternating projection method to solve it. To the best of our knowledge, we are the first to propose a method that solves RPCA problem without considering any objective function, convex relaxation, or surrogate convex constraints. We demonstrate through extensive numerical experiments on a variety of applications, including shadow removal, background estimation, face detection, and galaxy evolution, that our approach matches and often significantly outperforms current state-of-the-art in various ways.Comment: In the proceedings of Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Depth Superresolution using Motion Adaptive Regularization

Spatial resolution of depth sensors is often significantly lower compared to that of conventional optical cameras. Recent work has explored the idea of improving the resolution of depth using higher resolution intensity as a side information. In this paper, we demonstrate that further incorporating temporal information in videos can significantly improve the results. In particular, we propose a novel approach that improves depth resolution, exploiting the space-time redundancy in the depth and intensity using motion-adaptive low-rank regularization. Experiments confirm that the proposed approach substantially improves the quality of the estimated high-resolution depth. Our approach can be a first component in systems using vision techniques that rely on high resolution depth information