Imaging Theoretical And Technological Research Of Digital Holography Based On Compressive Sensing

Holography can obtain three-dimensional information of object by only one recording due to the ability of capturing the amplitude and phase.The holographic recording process of compressing the three-dimensional information to twodimensional information can be regarded as the compression of the imaging target signal.However,it is an ill-posed problem to recover three-dimensional information of an imaging target by using two-dimensional hologram which is captured by single recording.Compressive sensing can effectively solve the ill-posed problem and reconstruct high dimensional information from low dimensional information.Digital holography based on compressive sensing,namely compressive holography,solves the ill-posed problem of holographic imaging by using physical propagation model and sparse regularization condition to construct a compressive sensing model,which solves the problem of tomographic reconstruction of three-dimensional imaging target from only two-dimensional hologram.On the basis of analyzing the research status at home and abroad and limiting problems of digital holography based on compressive sensing,this thesis carries out systematic theoretical analysis,numerical simulation analysis and experimental verification for reconstruction time and axial resolution.The specific research contents and main innovations are as follows:（1）This thesis proposes a dimension reduction of measurement matrix method of digital holography based on compressive sensing for the reconstruction time problem of digital holography based on compressive sensing.Firstly,this thesis carries out the theoretical analysis of influence of measurement matrix of reconstruction time,and key factors are analyzed by numerical simulation.Then dimension reduction of measurement matrix method is studied and proposed.The proposed method is a general dimension reduction of measurement matrix framework and has sufficient extendibility,which is mainly composed of filter operator and parallel operator.In the dimension reduction of measurement matrix framework,hologram segmentation technology and parallel computing technology are used as the filter operator and parallel operator respectively,which can significantly reduce the reconstruction time and achieve high-quality tomographic reconstruction of three-dimensional imaging targets.Finally,the feasibility and effectiveness of dimension reduction of measurement matrix method of digital holography based on compressive sensing are verified by simulation analysis and optical experiments.Experimental results show that,compared with the traditional compressive holography method,the proposed method can achieve high quality reconstruction of specific targets,and achieve an average of 60 times of reconstruction acceleration under the condition of acceptable reconstruction quality.（2）This thesis proposes a compressive holography algorithm based on deep decoder for the axial resolution problem of digital holography based on compressive sensing.Firstly,the theoretical analysis of axial resolution of traditional compressive holographic reconstruction is carried out.Then a compressive holography algorithm based on deep decoder is proposed to solve the inverse problem of holographic imaging by using deep learning technology.The proposed method is untrained method and avoids the limiting problems of traditional optical imaging technology based on deep learning,including requirement of huge data set and matching sensitivity of training set and test set.In the compressive holography algorithm based on deep decoder,the minimization problem is constructed from the perspective of error estimation of back propagation for that the error estimation based on hologram may face the problem of similar solution.Finally,the reconstruction ability of threedimensional object of the proposed compressive holography algorithm based on deep decoder is analyzed and demonstrated by numerical simulation analysis and optical experiment,which provides the thinking direction of solving the similar solution problem and a theoretical and experimental basis for the axial resolution improvement of compressive holography.