| The classical sampling theory is based on Shannon-Nyquist theorem: the sampling rate must be at least twice higher than the maximum frequency in the signal. Recently a new sampling theory called compressive sensing asserts that in some cases the sampled signal can be well recovered far below the Nyquist rate. This applies to signals that are sparse in a given basis. Compressive sensing can be applied in many areas, such as signal precessing, imaging, earth probing, radar, and holography. In this thesis we introduce the basic concepts of compressive sensing and its application in coherent imaging and antenna synthesis. In coherent imaging we point out that we can acquire not only the amplitude but also the phase information of a phase object via compressive sensing. We also show that in antenna synthesis, compressive sensing can optimize the antenna design. |
