Research On Compressed Sensing Radar Imaging Method Based On Kronecker Product

In order to get high-resolution radar images, wideband signal is required to emit. Unfortunately, large bandwidth will increase the sampling frequency and the discrete echo data according to Nyquist sampling theorem, which not only improves the difficulty of data transmission, storage, processing, but also increases the hardware complexity. In recent years, compressed sensing(CS) theory suggested that the signal can be recovered high probability or accurately by under-sampled echo data under certain conditions. With CS theory, radar researchers put forward a new radar imaging method which called CS radar imaging that radar images can be recovered in less than the Nyquist sampling frequency. Due to vectorization of the 2-D scene, CS radar imaging method will spend a lot of time on optimization, which can not get radar images immediately and have low efficiency, so that this method can only handle small radar scenes.To solve low efficiency, high complexity of the conventional CS radar imaging method, many researchers continued to research and launched their studies, of which the main idea was that CS was employed to process the range or azimuth of radar scenes. Although it can improve the efficiency of imaging, it did not solve the problem essentially, because Nyquist sampling theorem was still needed to meet. So this paper, which combined matrix theory of Kronecker product with traditional CS radar imaging, proposed a novel CS radar imaging method based Kronecker product and analyzed its feasibility. And then we applied it to the inverse synthetic aperture radar(ISAR) and synthetic aperture radar(SAR) imaging.As we all known, ISAR is used for detection and imaging of aircraft, missiles, ships and other targets. In this situation the recovery targets can be considered sparse with respect to the whole scene. So the paper firstly assumed that ISAR scene was sparse. Then by analyzing the scene echo formula at ISAR turntable model, this paper established ISAR echo model based Kronecker product, and proposed CS-ISAR imaging method based on Kronecker product. To solve this model, the auxiliary variable was introduced to instead the azimuth result after observing scene, then we did sparse constraint to the azimuth of scene and the range auxiliary variables, which can be transformed into unconstrained optimization problems to solve by alternating direction method(ADM). Finally, experiments showed the superiority of this method: lower time complexity and high resolution.In the end, the paper applied Kronecker product to the SAR imaging. Due to complexity of SAR scene, we discussed sparse transformation under total variation(TV) domain before establishing SAR echo model based Kronecker product. And then this paper constructed CS-SAR imaging optimization model based on Kronecker product. Split-Bregman reconstruction method was employed to solve it. Since the method was operated directly on the scene matrix, we can avoid the vectorization of the 2-D scene, which significantly reduced the dimension of the measurement matrix and the computational complexity. Experiments verified the advantages of this method.