| Summary: | Sparse sampling and sparse arrays have attracted lots of interests in recent years. In this dissertation, we firstly apply nested sampling and co-prime sampling to ultra-wide band radar, which require us to extend the algorithms from stationary signals to non-stationary signals. After that, the synthetic aperture radar data is compressed through singular-value QR-decomposition algorithm. The dissertation also proposes an approach to turn low resolution images into high resolution (HR) images. We extend co-prime sampling structure to interpolation in order to improve the resolution of reconstructed images through compressive sensing (CS). Compared to the direct CS method and conventional interpolation method, the new co-prime interpolated compressive sensing (CopCS) approach could tremendously reduce the RMSE and improve the PSNR. Besides, in high compression ratio scenario, CS exhibits a poor resolution due to the included black dots, while CopCS can recover the image without intro ducing dots. Moreover, we also test CopCS approach on the Greenland b ed elevation raw data set (very sparse sampled). In addition, the augmented matrix approach from the minimum redundancy array (MRA) is extended to the sparse arrays – nested array and co-prime array for direction-of-arrival estimation. Especially when the background of the system model is in underwater environment and the sensors are considered as moving passive sonars. Numerical examples of how to construct these new structures of the non-uniform array are elaborated. Moreover, as sparse arrays cost fewer elements, two sparse cylindrical arrays are proposed in this dissertation. According to the characteristic of cylindrical array, it can be seen as a linear array whose elements are the identical circular arrays. Therefore the co-prime linear array and nested linear array could be combined with circular arrays. Based on the beam pattern of uniform cylindrical array, 1D and 2D beam pattern of co-prime cylindrical array and nested cylindrical array are derived ...
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