Image Measurement Matrix Optimization Based On Posterior Information And Unit Norm Tight Frame

Compressed sensing theory is a new theory of signal processing.With the sparsity of image signal,the theory integrates the sampling and compression into a single process,and the original signal is accurately reconstructed through choosing a appropriate algorithm.Compared with the traditional Nyquist sampling theorem,this theory reduces the signal sampling rate and the sampling resources' expense.For the image compression sensing,the measurement matrix plays a very important role in the sampling,compression and recovery of image signals.It is of great significance to design an excellent measurement matrix for signal reconstruction and the development of compressed sensing theory.In this thesis,the characteristics and performance of the measurement matrix are studied,and the innovations are shown as follows:1.Aiming at the lack of coherence of measurement matrix and low robustness,this thesis proposes an image measurement matrix optimization algorithm based on posterior information.Based on the traditional measurement matrix optimization model,the algorithm considers the posterior information composed of mean square error of image reconstruction,and uses it as a regular term.The central limit theorem and matrix singular value decomposition are used to respectively reduce the computational complexity and ensure the convergence of algorithm.Finally,the gradient descent method is used to solve the measurement matrix.Theoretical analysis and simulation experiments show that the newly proposed matrix optimization model not only reduces the mutual coherence between the measurement matrix and the sparse basis,but also makes full use of the information of the image itself.the measurement matrix becomes more robust and image reconstruction accuracy has been improved.To a certain extent,the noise immunity of the compressed sensing system is improved.2.With the consideration of the equiangular tight frame scale is easily limited and the Gram matrix cannot be guaranteed to be a semi-positive definite matrix in traditional spectral constraint set,a measurement matrix optimization algorithm based on the unit norm tight frame is proposed in this thesis.Firstly,a new unit norm tight framework is constructed by utilizing the projection iterative algorithm and the newly defined spectral constraint set with the foundation of the tight frame and the equiangular frame.Not only does the constructed frame have the structural and spectral characteristics,but itsdimensions are not limited by the matrix dimensions,and then the measurement matrix is optimized by this frame.Theoretical analysis and experimental simulations show that the proposed matrix optimization algorithm is simple to calculate,and can directly derive its analytical solution,which can solve the matrix approximation problem generated in the traditional optimization algorithm,and the complexity of the algorithm can be reduced.The optimized measurement matrix not only has low coherence between the atoms,but also gets a good tightness with its corresponding Gram matrix,and the robustness of the image compression sensing system is significantly enhanced.