Research On Measurement Matrix And Image Fusion In Compressed Sensing

Compressed sensing theory take advantage of the sparsely of signals by projecting the high-dimensional signals to low-dimensional data space. Compressed sensing can recover original signals from a small amount of sampling data by non-linear reconstruc-tion algorithm.So it can save storage space and bandwidth resources, can reduce times and storage space. Compressed sensing have got lots of attention, become a very popu-lar research field, have been applied in radar signal, remote sensing, and medical imag-ing, wireless networks, compressed sensing have a very broad application prospects. The construction of measurement matrices is an important part in compressive sensing. Compressed sensing sampling system are only a projection of measurement matrices, depend on measurement matrices, so a good measurement matrix is first. Compressed image fusion fuse the measurements of images, how to choose a good fusion parameter is a problem to be solved. Research results are as follows:(1) Deterministic construction of measurement matrices from Fourier matricesRandom part Fourier matrices use of FFT algorithm, can greatly reduce the com-putational complexity, but random part Fourier measurement matrices are complication and uncontrollable because of its randomness. A.Devore proposed deterministic mea-surement matrices, whose structure can be controlled, storage and applied more conve-nient, but size of measurement matrices is limited. Our idea is to combine the advan-tages of deterministic measurement matrices and random part Fourier measurement ma-trices, to construct a deterministic construction of measurement matrices from Fourier matrices, this measurement matrices are controlled. By m sequence from feedback shift register (Linear Feedback Shift Register, LFSR), we construct a pseudo-random inte-ger generation algorithm to generate the index sets, then we can construct deterministic construction of measurement matrices from Fourier matrices. By Gersgorin disk theo-rem and Weyl series theorem, we can prove that the deterministic measurement matrices meet RIP property and MIP property. By simulation experiments of one-dimensional and two-dimensional image signal, compare with the Gaussian measurement matrices, Hadamard measurement matrices etc. the same measurement M. and sparsely K, our deterministic construction of measurement matrices from Fourier matrices have higher success rate of recovery; In evaluation indexes of the squared error (MSE), root mean square error (RMSE), peak signal to noise ratio (PSNR) and structural similarity (SSIM) to get advantage.(2) Research on measurements characteristic and applied to the compressed image fusionBased on compressed sensing image fusion, can greatly improve the efficiency of data transmission and storage, to reduce the computational complexity, is an image fu-sion method. Compressed sensing imaging system is only a projection of the original signal, it depends on the measurement matrices. Research on measurements character-istics, find the connection measurements and the original image feature information by data analysis, which can use to select fusion parameter. Advantages of using the Parti-cle Swarm Optimization, we can propose a new compressed image fusion method that fusion parameter is selected by PSO whose fitness function is measurements charac-teristic.Simulation analysis compressed image fusion method what has been proposed advantages and disadvantages.