Theory Of Compressive Sensing And Its Application In Imaging

The military applications call for more stringent requirements for the accuracy, timeliness and diversity of information. As a key approach to acquire it, the imaging systems need a substantial performance increase, such as resolution enhancement. In the box of Shannon sampling theorem, raising the resolution means cutting the pixel size of sensor and increasing the number of pixels. This will enlarge the complexity and difficulty of system nonlinearly.Compressive sensing (CS) has given a revolutionary solution: Based on the sparsity of signal and sub-Nyquist non-coherent compressed sampling, one can recover the original signal by sparse optimization. It avoids the blind pursuit of an excessively high-resolution sensor. This paper investigates the theory of CS and its application in imaging system.In theoretical aspect, we have studied the Harmonic analysis based and data driven method for sparse representation. A contrast analysis of these methods is given by testing them on a typical database of remote-sensing images. Take the 1 -norm minimization as main factor, the models and algorithms of sparse recovery have been discussed. We have proposed a recovery condition based on cumulative mutual coherence (CMC), and given a theoretical upper bound of the recovery error. This recovery condition combines the advantages the mutual coherence (MC) and restricted isometry property (RIP). Meanwhile, we have extended the optimization criterion of measurement matrices by using CMC.Unlike the traditional imaging methods which begin with the matched filtering, we take the process of imaging as solving a Fredholm first kind integral equation. The theory of operators Hilbert space in employed to analyze the ill-conditioning of the solution. The constraint of sparsity is introduced to turn it to well-conditioned. After that, the measurement matrix is imported to finish the compressed sampling. Finally, the compressive imaging method is established. We have developed the performance analysis model of compressive imaging via modulation transfer function and error analysis of sparse recovery. The quantitative effects of sparsity of signal, amount of measurements, and noise on the accuracy of image reconstruction are given.As for practical aspect, firstly, we have considered several realization modes of optical compressive imaging. 1) We have proposed the compressive quantum imaging, and pointed out that the chaotic thermal lights satisfy the recovery condition. So, the quality of imaging can be enhanced thanks to the sparse recovery. 2) We have studied the high-resolution imaging based on focal plan coding. The technology of multiplexing and amplitude mask or (Digital Micro-mirror Device) DMD is used to complete the compressed sampling. A resolution-varied imaging mode is given. 3) We have discussed a low-data-rate imaging mode by using CMOS. The compressed sampling is finished by vector-matrix multiplication in analog domain, and the data rate is significantly reduced. Secondly, we have investigated the application of CS in radar system. 1) The target poisoning in multi-range-rate radar system. By the spline function modeling with knots optimization of the target trajectory, and systematic error estimation via sparse restriction, we have realized a high-precision trajectory solving method. 2) Random noise radar sparse image reconstruction, which can overcome the shortcoming that traditional imaging methods suffer from high background noise floor. Using the new method, one can achieve high-resolution unambiguous imaging even though the sampling rate is below Nyquist rate. 3) Low-data-rate (Inverse Synthetic Aperture Radar) ISAR imaging, in which compressed sampling is complete by multiplication of echoes with (0, 1) random sequences and integration. This will sufficiently reduce the needed rate for Analog-to-Digital conversion. The 1-norm minimization is utilized to high accuracy image reconstruction.