In this thesis a novel edge detection technique is developed that employs compressed sensing image reconstruction techniques. The ability of compressed sensing noise reduction is combined with wavelet transforms, acting both as a sparsifying transform as well as an edge detection media. The proposed design was implemented and simulated on a brain phantom. The simulation results were provided for a variety of different sets of variables, and the differences were explained. The results obtained are compared with other edge detection techniques already in use. One important comparison criteria is the visual quality of images; according to which the proposed technique presents improved noise reduction and edge preservation. In addition to qualitative evaluation a method of quantitative measurement based on structural content is also utilized. It is found that the values for such a measure of the proposed method is 1.0755, 1.0174 and 0.5590 for Gaussian, Speckle, and Salt & Pepper noise types respectively. These results indicate that this novel method also improves edge preservation, while the visual quality inspection indicates how much noise has been suppressed.