Research On Signal Reconstruction Technology And Imaging System Based On Compressed Sensing

With the rapid development of information technology,the modern society has put forward higher and higher requirements for the speed and accuracy of signals processing.In traditional signal processing,signal sampling must satisfy the Nyquist sampling theorem to ensure that the original signal can be restored.Compressed sensing(CS)theory was proposed in 2006,and the biggest advantages of compressed sensing are to sample the signal at a rate lower than the Nyquist sampling frequency and to accurately recover the original signal from such a sampled signal.Therefore,the lower data sampling amount required by CS greatly saves the cost of signal transmission and processing,which is very significant for the development of information technology at both the hardware and software.The research work of this thesis is funded by the "West Light Foundation for Innovative Talents of Chinese Academy of Sciences" and other foundation projects.In the research,based on the basic theory of compressed sensing,the CS-based measurement sampling and signal reconstruction are performed on discrete signals,and the proposed new algorithms improve the CS-based signal reconstruction technology.Furthermore,based on the basic theory of compressed sensing image reconstruction,a single-pixel imaging system was established for taking single-pixel imaging of the real scenes,and the real-time single-pixel video imaging is conducted by the method of deep learning for improving the imaging quality and imaging frame frequency.The research works of this dissertation include the five aspects: signal sparse transformation,measurement matrix construction,reconstruction algorithm,projection method and single-pixel imaging technology.The corresponding innovation methods are proposed in these five areas,and the following contents are the research contributions of this dissertation.(1)The signal sparsifying in compressed sensing.In this dissertation,discrete wavelet transform(DWT)is used to represent non-sparse signals by sparsity transformation.According to the characteristic that the wavelet coefficients of non-sparse signals present an approximate exponential decay distribution,a new constraint condition of DWT is proposed in this dissertation,and a corresponding constraint diagonal matrix with exponentially decayed diagonal elements is designed.This new method can impose a shaping constraint and make wavelet coefficients closer to a true exponential decay distribution on the basis of the approximate exponential decay of original wavelet coefficients,making wavelet coefficients become more sparse and improving the performance of DWT,which are beneficial to CS sparse reconstruction.For image reconstruction,the experimental results of the block modulation and the column modulation are compared,and the column modulation is chosen for CS image reconstruction as a matter of priority.The proposed novel method of wavelet sparsity basis optimization can effectively improve the CS signal reconstruction accuracy and image reconstruction quality.(2)Compressed sensing measurement matrix construction.Based on the principles of Gram matrix incoherence and sensing matrix construction,a novel objective loss function model is designed according to Gram matrix and sensing matrix,the new objective function does not only optimize the measurement matrix based on the incoherence property of the measurement matrix,and also a new measurement matrix initialization method that can be adapted to this new objective function is proposed,finally the gradient projection strategy is employed to solve the new objective function for acquiring the new measurement matrix.Compared with the classical measurement matrix construction methods and some recent measurement matrices that are designed via data-driven and deep learning,this proposed method not only can learn to construct a new measurement matrix that is adaptive to the known sparsity basis with the lower mutual coherence,but also the new method can achieve better performance of signals reconstruction for both one-dimensional sparse signals and two-dimensional image signals.(3)Image projection and single-pixel imaging method.The single-pixel imaging system is built based on the CS theory,in which a digital micromirror array DMD(Digital Mirror Device)is used to encode and sample the imaging scene signals,according to the encoding characteristics of DMD on the plane signal of the imaging scene,a bilateral projection method based on column modulation is proposed for image measurement and image reconstruction.This bilateral projection method can conduct the measurement process for both image column and row information in parallel,which can make full use of not only the correlation information between image rows or columns but also the global sparseness of the image plane,and the structure information of the whole image is sampled more evenly,the accuracy of reconstructed images at low sampling rate can be significantly improved by the bilateral projection method.This bilateral projection is applied to single-pixel imaging,so that images of high quality can be reconstructed at lower sampling compression ratio,so single-pixel imaging can be performed at lower sampling rates.(4)Compressed sensing reconstruction algorithm.Based on the respective characteristics of the minimum norm based convex optimization and non-convex optimization algorithms,a new mathematical model on the basis of the L2 norm is designed.Through dynamic adjustment of the model parameter,this new mathematical model can iteratively approximate a smooth L0 norm from an approximate L2 norm.A new objective loss function is proposed from the new mathematical model and is solved by the gradient descent method.The proposed method can get close to the global optimal and approximate L0 sparsity solution with greater probability and higher efficiency in algorithm reconstruction.Compared with some classic reconstruction algorithms and some recent reconstruction algorithms,the new algorithm can reconstruct the images of higher accuracy and achieve single-pixel imaging of higher quality in very short time.(5)Deep learning based real-time single-pixel imaging.According to the proposed image bilateral projection method,an optimized deep convolutional neural network architecture is designed based on the Residual Network(Res Net),and the deep learning image reconstruction technology is applied to the single-pixel imaging.The designed network is trained on the image data set,which simulates the single-pixel imaging process of the bilateral projection method.Finally,the learned network is used to reconstruct the image according to the imaging measurement data,completing the single-pixel imaging process.Compared with the classical CS reconstruction algorithms and the recent deep learning single-pixel imaging methods,the proposed method can effectively improve the single-pixel imaging quality at low sampling rates(6.25% and4%).In addition,benefit from the extremely short image reconstruction time of deep learning method and the shorter DMD measurement time of 0-1 binary measurement matrix,the real-time single-pixel video imaging with the resolution of 128×128 and256×256 is realized respectively through single-channel and four-channels modes at the 4% sampling rate.