Research On High Resolution Image Reconstruction Technology Based On Compressed Sensing

The rapid development of information technology makes people increase the demand for information,signal conversion from analog to digital has always been strict compliance with the requirements of the Nyquist sampling theorem,the sampling rate must reach more than 2 times the bandwidth of the signal,which makes the signal can be accurately reconstructed.The efficient transmission and storage of data also impose stringent requirements for compression technology.In order to reduce the cost of transmission,processing and storage,such high-speed sampling and recompression process wastes a lot of sampling resource.And in 2006,Donoho and Candès put forward the theory of compressed sensing,CS.The compression representation of the signal is directly obtained,which ensures that the information is sampled much lower than the Nyquist sampling without any loss of information,and the signal can be reconstructed accurately.The process of the compression sensing is to obtain the low dimensional measurement value by the measurement matrix first,and then the high dimensional original signal is reconstructed by the reconstructed algorithm using the measured value.Because the reconstructed algorithm is a solution process from low dimension signal to high dimension signal,we must solve an underdetermined equation,which requires that the original signal is sparse or can be expressed in sparse terms.So the theory of compressed sensing is mainly composed of three parts: the sparse representation of signal,design of measurement matrix and reconstruction algorithm.This paper is carried out from the three parts,aiming at reducing the image sampling rate and improving the quality of image reconstruction,by constantly improving and optimizing these three parts.The main work is as follows:First,we use compressed sensing to reconstruct the signals with different sparsity,analyze and compare the influence of signal sparsity on the final signal reconstruction accuracy and success rate.The experimental simulation results show that the better the sparsity of the signal is,the better the reconstruction of the signal is.The traditonally and usually used methods of making signal sparse are discrete Fourier transform(FT),discrete cosine transform(DCT)and discrete wavelet transform(DWT).And the sparse representation capabilities of these three sparse transformations are quantitatively compared and qualitatively analyzed,and wavelet transform with the best sparse representation ability is chosen as the sparse basis.Second,we need to measure the image linearly to reconstruct the original signal,and the signal is not only sampled,but also compressed,and the dimension of signal is greatly reduced.Based on the binary random measurement matrix,the measurement matrix is redesigned.A very sparse diagonal block measurement matrix is constructed,which greatly improves the mutual incoherence property of the matrix and makes the sensing matrix better satisfy the restricted isometry property(RIP).The new measurement matrix is not only easy to implement in hardware,but also speeds up the reconstruction speed of the image,and also improves the reconstruction precision of the image.Third,we reconstruct the original signal by the reconstruction algorithm,and the quality of image reconstruction is largely determined by the reconstruction algorithm.On the basis of the minimum L0 norm non convex optimization algorithm and convex optimization algorithm,a new reconstruction algorithm approximating the smoothed L0 norm is put forward combining the advantages of convex optimization algorithm and non convex optimization algorithm.This algorithm accelerates the speed of image reconstruction,and improves the peak signal to noise ratio(PSNR)and structural similarity(SSIM)of the reconstructed image.To sum up,although the theory of compression sensing only appears in a short time,it has been a hot research direction in recent years in the world.At present,researchers have developed a wide range of application research for compressed sensing in lots of areas.In this paper,the improvement of three parts of the theory structure of compression sensing is descripted in detail to reconstruct as high quality images as possible under as low as possible measurement sampling rate,and the single pixel super resolution imaging of outdoor scene is preliminarily completed.Using this advantage,it lays the foundation for the detection of extremely far target,extremely dim and extremely weak signal and completing photon level super-resolution imaging,which also provides a reference and engineering theoretical support for the application of compressed sensing in a wider range.