We are going to present a fast iterative implementation of the Orthogonal Greedy Algorithm which can be used for any frames admitting fast decomposition - reconstruction procedures (wavelet frames, redundant discrete Fourier transform, redundant Walsh transform, etc.).

We show that, using OGA for wavelet frames, we need up to 1.45 times less expansion terms for image representation than for regular wavelet bases.

We also are going to show how this and one different algorithm can be use for solving the recently formulated problem of Compressed Sensing (Donoho, 2004).