M.Sc Student | Shoham Neta |
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Subject | Exploiting Sparse Representation for Discriminative Tasks |

Department | Department of Applied Mathematics |

Supervisor | Professor Michael Elad |

This thesis deals with the exploiting of sparse and redundant representations for solving separation problems. The goal of this research is to develop new methods for dictionary design and sparse decomposition that are optimally suitable for separation problems. In this work we focused on two separation problems.

The first problem is known under the name of source separation. In this problem we are given a sum of two signals, and we assume that for each signal there exists a sparse representation under different dictionary. The separation of this sum is made by finding sparse representations, simultaneously for both signals. Previous work on this subject proposed iterative algorithms that in each iteration perform sparse coding according to a different dictionary. Our main contribution here is the introduction of a new algorithm for separation. This algorithm perform sparse decomposition according to the two dictionaries simultaneously and requires only one iteration of sparse coding and which in spite of its simplicity gives competitive results relatively to the results of the existing algorithms, which carry much more complexity.

The second contribution of this research is the introduction of a new method for dictionary design in a discriminative manner. Such dictionaries are optimally designed for the classification task. As an example of a classification problem we took the texture segmentation task. In previous works it was shown, that by finding a representative dictionary for each texture, one can achieve a good segmentation. In this work we developed a new algorithm for discriminative dictionary learning, which helps us to achieve better segmentation results.