The Compressive Sensing (CS) as a novel acquisition approach that finds its usage in image processing. The hypothesis like this one assures signal recovery with high quality from decreased number of samples compared with the number required by the Nyquist - Shannon sampling theorem. It includes a gathering of strategies for representing a signal that are based on the predetermined number of estimations and after that signal reconstruction. The CS has been broadly utilized and applied in numerous applications including computed tomography, WiFi communication, image processing and camera design. Complex mathematics is developed in order to ensure signal reconstruction from relatively small information. Two commonly used groups of the algorithms are convex optimization and greedy approaches.