Research On Quantitative Differential Phase Contrast Imaging Based On Regularization

Quantitative differential phase contrast（q DPC）reconstruction is a typical non-interference quantitative phase reconstruction method.Through a simple critical illumination structure,combined with optical coding and establishment of the forward physical model,the phase of the target can be quantitatively reconstructed by single-step deconvolution.The penalty coefficient of the traditional q DPC algorithm based on L₂-norm regularization（also known as Tikhonov regularization）is affected by the experimental environment noise,which leads to poor robustness of phase reconstruction.Therefore,this method only has the function of"phase imaging",but loses the function of"quantitative reconstruction",which limits its application and development in quantitative phase imaging（QPI）.In order to keep the penalty term at a stable level and realize the quantitative measurement of q DPC,many subsequent studies have optimized the imaging optical path and forward model,including illumination coding improvement,mask aperture coding supplement,and optimization of phase transfer function（PTF）.However,for the final inverse problem of q DPC reconstruction,there are few reports to explore the optimization of phase deconvolution.Currently,only another commonly used regularizer,the total variation（TV）term,is introduced into the q DPC method to improve the reconstruction quality.Therefore,this thesis focuses on optimizing q DPC phase deconvolution and explores the influence of regularization terms on q DPC reconstruction.The specific research contents are as follows:（1）The L₀-q DPC reconstruction algorithm based on L₀-norm regularization is proposed for sparse samples.The principle derivation of L₀-q DPC is given based on the half-quadratic splitting（HQS）framework.The effects of the main penalty termαand introduced parameterβon TV-q DPC and L₀-q DPC reconstruction in HQS framework are analyzed in detail through simulation.Taking quantitative phase target（QPT）as an example,the optimal parameters of TV-q DPC and L₀-q DPC reconstruction are given.（2）It is found that the DPC image has dark-field sparse prior（DSP）,and a DSP-q DPC algorithm with compound regularizers is proposed.11 images of standard data sets are simulated by q DPC reconstruction,and the results of four q DPC algorithms with different constraints,including L₂-norm,TV norm,L₀-norm,and compound regularizers based on DSP,are compared.Those results prove that DSP-q DPC is universal for any DPC image.（3）The performances of the above four q DPC reconstruction algorithms with different regularizers in phase fidelity,imaging resolution,and contrast are compared through experiments.The feasibility of various algorithms in biomedical application is explored through the applications of three-dimensional imaging of biological cells,dry mass density inversion,and real-time phase imaging.Moreover,the strong robustness,high phase fidelity,and good imaging contrast of the proposed DSP-q DPC algorithm are demonstrated.At present,there are few researches on the optimization of phase deconvolution in q DPC reconstruction.As an exploratory work in this field,there have been some preliminary results.The improvement of regularization belongs to the mathematical optimization theory,and there is no need to change the system optical path,components,and even the physical model.As a relatively independent scheme,this study is expected to provide a new idea for the improvement and development of q DPC reconstruction methods in the future.