Data models are a cornerstone of contemporary methodology in the field of signal and image processing which have evolved over the years. In that respect, the past decade has been certainly the era of sparse and redundant representations, a popular and highly effective data model. The main objective of this dissertation is the performance improvement of this model in image restoration and reconstruction. To this end, we first consider the performance improvement of sparse coding for noisy images for which low-rank and nonlocal sparse representation models are proposed. These models leads to superior image denoising performance compared to the state-of-the-art methods. Second, we concentrate on the dictionary as the core component of sparse representation model. To improve the performance of learned dictionaries for sparse representation, a coherence regularized dictionary learning model is presented and two novel dictionary optimization algorithms are proposed. Furthermore, we propose a boosted dictionary learning approach to train a dictionary ensemble which results in more efficient sparse representations. Lastly, a joint sparse model is presented to train multiple dictionaries from different datasets taking into account their relationships. Key Words Sparse representation, dictionary learning, sparse coding, image restoration, optimization.
