Image Compression And Reconstruction Based On Low-Coherence Projection Matrix And Adaptive Sampling Rate

Compressive sensing theory is a new image compression tool,which breaks the constraints of Nyquist sampling theorem on sampling frequency.Compressive sensing theory utilizes the sparsity of the signal to perform the sample and compress of the signal simultaneously,and then the original signal is recovered accurately through different reconstruction algorithms.The projection matrix plays a key role in the process of image signal compression,which greatly affects the performance of image signal compression and reconstruction.The sampling rate has a decisive effect for image reconstruction.And different sampling rates are obtained by sampling adaptively according to the characteristics of different image blocks can effectively improve image compression performance.To this end,an optimization of the projection matrix and adaptive sampling rate are studied in this thesis.The main innovations of this thesis are as follows:1.In order to reduce the coherence between the observation matrix and the sparse basis matrix,and improve the robustness of the compressed sensing system,an observation matrix optimization algorithm based on the tight frame and sparse representation error is proposed in this thesis.Firstly,the average mutual coherence of the sensing matrix is reduced by the Gram matrix which approximates to the unit matrix and the constructed tight frame.Secondly,the sparse representation error as a regularization term is added to the conventional optimization model to improve the robustness of the observation matrix.Finally,the analytical solution is applied to solving the projection matrix to ensure the convergence of the algorithm.Experimental results show that,the average mutual coherence of the projection matrix can be reduced at least0.03 with the matrix optimization algorithm proposed,and the constructed observation matrix is more robust.2.To solve the problems that sampling resources distributed unevenly and wastefully,and in order to improve the single sampling mechanism and the inflexible allocation of observation resources for the adaptive sampling rate,an adaptive sampling rate algorithm based on natural exponential decay is proposed.The algorithm firstly divides the image into the same size to reduce the computing and storage pressure of the device.Then based on the posterior SSIM index of the reconstructed image block,different sampling rates are allocated to ensure that the global information of image is considered in the new adaptive mechanism.Finally,the natural exponential decay function is introduced to design a variable step size projection matrix search mode to ensure the convergence speed of the algorithm.The experimental results show that the proposed adaptive sampling rate algorithm has better reconstruction performance than the fixed sampling rate algorithm.