| Compressive sensing is a novel emerging theory of signal acquisition and processing, which break through the limitations of the traditional Shannon/Nyquist sampling theorem, the main benefit from that the vast majority of signals in the nature generally has the prior knowledge of sparsity, which can help to reconstruct the original signal accurately from the far less linear incoherent measurements than the Nyquist sampling rate. Obviously, recovering the real signal from incomplete measurement data is an ill-posed inverse problem. Compressive sensing theory has a huge potential value in many areas ranging from most signal processing applications, such as the field of information theory, signal processing, optical imaging, pattern recognition, signal acquisition and communications.Compressive imaging is one of the most important research areas of compressive sensing theory, the first successful instance of compressive imaging applications is the single pixel camera designed by Rice University based on compressed sensing theory which use only one detector for scene imaging. The camera has a control of digital micro-mirror array, driven by a pseudo-random binary array, and reflects the the scene of interest onto a single detector array which gather the intensity of this projection, and then reconstruct the original image from the observation value. A major advantage of this structure is any binary projection matrix can be easily implemented in this imaging system, so that the compressed sensing theory can be naturally applied to the measurement. Single-pixel camera perfectly agrees with the compressive sensing theory, which using a random modulation only to obtain a measured value, and has successfully gained practical application in a small part of the imaging area such as Terahertz imaging. However, the most severely drawback of the single-pixel camera is that can only obtain a measured value at one time, however, in other more extensive high-resolution applications, the time to obtain sufficient measurements is too long and thus is not very practical. Therefore, Stern proposed an improved compressive imaging method, that all measured values can be obtained with a single exposure conditions, and has greater potential application in other more widely imaging areas.This thesis draws on Stern's single exposure ideology, surrounded with a series of problems encountered in compressive imaging theories and methods, imaging architecture, physical realizable imaging system and three-dimensional compressive imaging theory for deeply research.The main research works and contributions of this thesis are outlined as follows.1) A novel imaging system consisting of double lens and deterministic optical phase mask is proposed, and the basic principles and formulas for compressive imaging are described, and the validity of the phase mask imaging method with Toeplitz and Circulant two deterministic phase mask matrix for instance is verified in the numerical simulations. Compared with the random phase mask modulation compressive imaging method with single-exposure proposed by Stern, using Toeplitz and Circulant and other deterministic phase mask matrix are more conducive to physical implementation and fast calculation. In addition, any two columns of measurement matrix are corresponding to compressive imaging system consisting of double-lens and deterministic phase mask to meet some basic conditions and specific derivation analysis are derived.2) Several novel random spacing sparse measurement matrices, including the random spacing sparse Toeplitz/Circulant and random ternary spacing sparse Toeplitz/Circulant matrices are proposed, and the proofs for such measurement matrices to satisfiy the restricted isometric property are given. Compared with the Gaussian measurement matrices, the novel proposed matrices, independent component and storage spaces are reduced significantly, and the speed of reconstruction have greatly improved; then these novel types of random spacing sparse measurement matrices are applied into compressive double lens imaging system, the validity of them as a phase mask matrices to achieve image information random modulation is verified; The simulation results of proposed random spacing sparse phase mask matrix demonstrate that proposed masks is superior for its easier physical implementation, low storage capacity, ease of data transfer; and with the same reconstruction performance and the significantly reduced reconstruction time, which has great significance for practical application of compressed sensing theory. In addition, blocked measurement matrices as the phase mask matrices are also proposed, which have the advantage of easy physical implementation, and are more suitable for multi-channel imaging applications, and can help compressive imaging theory to practical application.3) Compressive sensing was introduced into image super-resolution reconstruction problem, numerical simulation results demonstrate that reconstruction from low resolution to high resolution with different blurring kernel, that are much better than the direct interpolation method. In addition, an improved optical imaging method based on the4-f Fourier frequency domain phase random encoding for compressed imaging is proposed, which can capture image information and recover the image effectivrly;Due to the measured values recorded in real-world should satisfy non-negative constraints, the convolution principle to analysis the basic principle for how to implementing the measurement values non-negative is analysized, and an improvement frequency domain phase encoding imaging method is proposed to implement non-negative recording of the measurement values and successful reconstruction after then, which is conducive to large-scale image compressed encoding and reconstruction, and its practical application and promotion. For the realization of actual mask, an improved encoding of binary random phase mask is also given in this thesis, to avoid the practical difficulty for producing uniform random phase mask.4) A Fourier optical imaging architecture based on the4-f0/1frequency domain amplitude mask aperture imaging method with random spacing grating or evenly spaced grating combined are proposed. Compared with the traditional pinhole camera, the utilization of illumination light can be greatly increased in our method to improve the robustness against noise. Compared with the random phase mask encoding, the amplitude coded aperture are much easier for physical implementation. Based on this point, an improved frequency-domain amplitude0/1mask aperture compressive imaging system is designed, non-negative constraints is guaranteed, making a better consistency between the actual physical measurement matrices and the theoretical calculation of the measurement matrices.5) Compressed sensing theory is applied in three-dimensional imaging, and a multi-wavelength compressive holography method is proposed which can reconstruct a3D coherent tomography imaging from a two-dimensional hologram; compressive imaging method with single wavelength speckle incoherent is extended to multi-wavelength, and compressive holography imaging is also applied into sparse aperture synthetic holography imaging which improves the phase instability problems encountered in sparse aperture synthetic holography imaging for mosaics of multiple low-resolution and low cost2D sensor arrays which can achieve large aperture; and the effectiveness of compressive holography imaging method is verified by physical experiments.
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