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

Decomposition Approach for Low-Rank Matrix Completion and Its Applications

In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into sub-matrices which are filled with a proposed trimming step and then are recombined to form a low-rank completed matrix. The divide-and-conquer approach can significantly reduce computation complexity and storage requirement. Moreover, the proposed decomposition method can be naturally incorporated into any existing matrix completion methods to attain further gain. Unlike most existing approaches, the proposed method is not based on norm minimization nor on SVD decomposition. This makes it possible to be applied beyond real domain and can be used in arbitrary fields, including finite fields. The effectiveness of our proposed method is demonstrated through extensive numerical results on randomly generated and real matrix completion problems and a concrete application-video denoising. The numerical experiments show that the algorithm can reliably solve a wide range of problems at a speed significantly faster than recent algorithms. In the proposed denoising approach, we 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, our approach outperforms state-of-the-art denoising techniques such as VBM3D and 3DWTF in terms of both time and quality. Our technique also achieves significant improvement over time against other matrix completion methods