Sparse Representation is a topic that has been gaining popularity in recent years due to its efficiency, performance and its applications in communication and data extraction fields. A number of algorithms exist that can be used to implement sparse coding techniques in different fields which include K-SVD, ODL, OMP etc. In this project one of the most popular sparse algorithms, the OMP (Orthogonal Matching Pursuit) technique, is investigatedin depth. Since OMP is not capable of finding the global optimum, a Top-Down Search (TDS) algorithm is proposed in this project to achieve much better results by sacrificing the execution time. Another contribution of this project is to investigate the properties of dictionary by modifying the frequency and shifting the phase of a standard Discrete Cosine Transfer (DCT) dictionary. The results of this project show that the performance of sparse coding algorithm still has room for improvement using new techniques.