Research On Measurement Matrices Of CS And Its Imaging Application

With the explosion development of compressive sensing in signal and information processing area, CS theory is triggering strong interests and research enthusiasms of both scientists and engineers. CS theory mainly includes three aspects:start with the sparse or compressive signal is projected onto random measurement matrix, and a few non-coherent linear projection coefficients are captured. Then make use of these coefficients to encoding the signal. At last, the original signal is reconstructed via a certain type of linear or nonlinear reconstruction strategy. The reason why CS theory is general is that under normal circumstances, signal or image data inherent has some sparse or compressible characteristics on the structure. The coefficients which contain most of the information of signal for a small scale can be obtained from the incoherent random projection directly. This means that realize sampling and compression synchronously. So construction the appropriate projection (measurement) matrices and design for the efficient reconstruction algorithm are two core task of CS theory. Nowadays, people’s demands for information are growing up day by day, and the emergence of CS theory breaks through the bottleneck of traditional Shannon sampling theorem. However, although the researches of basic theory and system validations of CS are already carried out at home and abroad, but the establishment of perfect system still needs much more time and many questions remain open.In view of the existing measurement matrixes such as Gaussian random matrixes and Bernoulli matrixes have plenty of weakness, for instance need much memory space, complex hardware realization, et al. The reconstruction algorithm such as minimum11norm method and matching pursuit can not ensure that both speed and fidelity meet the requirements at the same time, especially in the situation that large scale image is recovered. To the above questions, this paper is working on the construction of measurement matrixes, the research of reconstruction algorithms and imaging applications. The main work been done is as follows:1) Based on the concept of sparse signal, two important conditions such as incoherence and restricted isometry property are introduced respectively when constructing measurement matrix; summarizes the construct methods of several frequently-used random and determinacy measurement matrixes and their improvement approaches; analyzes the ideas of some classical reconstruction algorithms.2) A new measurement matrix based on Chirp encoding is constructed, and Chirp matrix meets RIP constraint is proved mathematically. With the aid of the special structure of Chirp matrix which is convenient for Fast Fourier Transform, two fast reconstruction algorithms:single pass and full pass are proposed; through two groups of simulation experiment with noise and not, the results demonstrate that the signal recovery performance of the reconstruction algorithm based on Chirp matrix can be comparable with that of matching pursuit; further optimization of this algorithm improving the reconstruction speed greatly without changing the reconstruction fidelity, which is benefit to the application of2D image.3) According to the concept of compressed imaging, the properties what effective measurement matrixes should have are given out; a much sparser and more universal measurement matrix is got through three improvements to Hadamard matrix. The theory analysis of improved Hadamard matrix shows that it can meet the requirements of measurement matrix in compressed imaging; through the simulation of three measurement matrix (Gaussian random matrix, improved Hadamard matrix, circulation banding sparse matrix), the performance of several reconstruction algorithm are compared, the results demonstrate that the improved Hadamard matrix can produce better compressive imaging performance and lower calculation cost; and the research on determinacy measurement matrixes is also benefit to physical realization of CI imaging system.