Full-color imaging is essential in digital pathology for accurate tissue analysis.Utilizing advanced optical modulation and phase retrieval algorithms,Fourier ptychographic microscopy(FPM)offers a powerful solution fo...Full-color imaging is essential in digital pathology for accurate tissue analysis.Utilizing advanced optical modulation and phase retrieval algorithms,Fourier ptychographic microscopy(FPM)offers a powerful solution for high-throughput digital pathology,combining high resolution,large field of view,and extended depth of field(DOF).However,the full-color capabilities of FPM are hindered by coherent color artifacts and reduced computational efficiency,which significantly limits its practical applications.Color-transferbased FPM(CFPM)has emerged as a potential solution,theoretically reducing both acquisition and reconstruction threefold time.Yet,existing methods fall short of achieving the desired reconstruction speed and colorization quality.In this study,we report a generalized dual-color-space constrained model for FPM colorization.This model provides a mathematical framework for model-based FPM colorization,enabling a closed-form solution without the need for redundant iterative calculations.Our approach,termed generalized CFPM(gCFPM),achieves colorization within seconds for megapixel-scale images,delivering superior colorization quality in terms of both colorfulness and sharpness,along with an extended DOF.Both simulations and experiments demonstrate that gCFPM surpasses state-of-the-art methods across all evaluated criteria.Our work offers a robust and comprehensive workflow for high-throughput full-color pathological imaging using FPM platforms,laying a solid foundation for future advancements in methodology and engineering.展开更多
Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)at...Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)attached to f.In this paper,we study the mean value distribution over a specific sparse sequence of positive integers of the following sum∑(a^(2)+b^(2)+c^(2)+d^(2)≤x(a,b,c,d)∈Z^(4))λ_(sym^(j))^(i)f(a^(2)+b^(2)+c^(2)+d^(2))where j≥2 is a given positive integer,i=2,3,4 andαis sufficiently large.We utilize Python programming to design algorithms for higher power conditions,combining Perron's formula,latest results of representations of natural integers as sums of squares,as well as analytic properties and subconvexity and convexity bounds of automorphic L-functions,to ensure the accuracy and verifiability of asymptotic formulas.The conclusion we obtained improves previous results and extends them to a more general settings.展开更多
Fourier Ptychographic Microscopy(FPM)is a high-throughput computational optical imaging technology reported in 2013.It effectively breaks through the trade-off between high-resolution imaging and wide-field imaging.In...Fourier Ptychographic Microscopy(FPM)is a high-throughput computational optical imaging technology reported in 2013.It effectively breaks through the trade-off between high-resolution imaging and wide-field imaging.In recent years,it has been found that FPM is not only a tool to break through the trade-off between field of view and spatial resolution,but also a paradigm to break through those trade-off problems,thus attracting extensive attention.Compared with previous reviews,this review does not introduce its concept,basic principles,optical system and series of applications once again,but focuses on elaborating the three major difficulties faced by FPM technology in the process from“looking good”in the laboratory to“working well”in practical applications:mismatch between numerical model and physical reality,long reconstruction time and high computing power demand,and lack of multi-modal expansion.It introduces how to achieve key technological innovations in FPM through the dual drive of Artificial Intelligence(AI)and physics,including intelligent reconstruction algorithms introducing machine learning concepts,optical-algorithm co-design,fusion of frequency domain extrapolation methods and generative adversarial networks,multi-modal imaging schemes and data fusion enhancement,etc.,gradually solving the difficulties of FPM technology.Conversely,this review deeply considers the unique value of FPM technology in potentially feeding back to the development of“AI+optics”,such as providing AI benchmark tests under physical constraints,inspirations for the balance of computing power and bandwidth in miniaturized intelligent microscopes,and photoelectric hybrid architectures.Finally,it introduces the industrialization path and frontier directions of FPM technology,pointing out that with the promotion of the dual drive of AI and physics,it will generate a large number of industrial application case,and looks forward to the possibilities of future application scenarios and expansions,for instance,body fluid biopsy and point-of-care testing at the grassroots level represent the expansion of the growth market.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12104500 and 82430062)the Key Research and Development Projects of Shaanxi Province(Grant No.2023-YBSF-263),the Shenzhen Engineering Research Centre(Grant No.XMHT20230115004)the Shenzhen Science and Technology Innovation Commission(Grant No.KCXFZ20201221173207022).
文摘Full-color imaging is essential in digital pathology for accurate tissue analysis.Utilizing advanced optical modulation and phase retrieval algorithms,Fourier ptychographic microscopy(FPM)offers a powerful solution for high-throughput digital pathology,combining high resolution,large field of view,and extended depth of field(DOF).However,the full-color capabilities of FPM are hindered by coherent color artifacts and reduced computational efficiency,which significantly limits its practical applications.Color-transferbased FPM(CFPM)has emerged as a potential solution,theoretically reducing both acquisition and reconstruction threefold time.Yet,existing methods fall short of achieving the desired reconstruction speed and colorization quality.In this study,we report a generalized dual-color-space constrained model for FPM colorization.This model provides a mathematical framework for model-based FPM colorization,enabling a closed-form solution without the need for redundant iterative calculations.Our approach,termed generalized CFPM(gCFPM),achieves colorization within seconds for megapixel-scale images,delivering superior colorization quality in terms of both colorfulness and sharpness,along with an extended DOF.Both simulations and experiments demonstrate that gCFPM surpasses state-of-the-art methods across all evaluated criteria.Our work offers a robust and comprehensive workflow for high-throughput full-color pathological imaging using FPM platforms,laying a solid foundation for future advancements in methodology and engineering.
文摘Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)attached to f.In this paper,we study the mean value distribution over a specific sparse sequence of positive integers of the following sum∑(a^(2)+b^(2)+c^(2)+d^(2)≤x(a,b,c,d)∈Z^(4))λ_(sym^(j))^(i)f(a^(2)+b^(2)+c^(2)+d^(2))where j≥2 is a given positive integer,i=2,3,4 andαis sufficiently large.We utilize Python programming to design algorithms for higher power conditions,combining Perron's formula,latest results of representations of natural integers as sums of squares,as well as analytic properties and subconvexity and convexity bounds of automorphic L-functions,to ensure the accuracy and verifiability of asymptotic formulas.The conclusion we obtained improves previous results and extends them to a more general settings.
基金National Natural Science Foundation of China(No.12574332)the Space Optoelectronic Measurement and Perception Lab.,Beijing Institute of Control Engineering(No.LabSOMP-2023-10)Major Science and Technology Innovation Program of Xianyang City(No.L2024-ZDKJ-ZDCGZH-0021)。
文摘Fourier Ptychographic Microscopy(FPM)is a high-throughput computational optical imaging technology reported in 2013.It effectively breaks through the trade-off between high-resolution imaging and wide-field imaging.In recent years,it has been found that FPM is not only a tool to break through the trade-off between field of view and spatial resolution,but also a paradigm to break through those trade-off problems,thus attracting extensive attention.Compared with previous reviews,this review does not introduce its concept,basic principles,optical system and series of applications once again,but focuses on elaborating the three major difficulties faced by FPM technology in the process from“looking good”in the laboratory to“working well”in practical applications:mismatch between numerical model and physical reality,long reconstruction time and high computing power demand,and lack of multi-modal expansion.It introduces how to achieve key technological innovations in FPM through the dual drive of Artificial Intelligence(AI)and physics,including intelligent reconstruction algorithms introducing machine learning concepts,optical-algorithm co-design,fusion of frequency domain extrapolation methods and generative adversarial networks,multi-modal imaging schemes and data fusion enhancement,etc.,gradually solving the difficulties of FPM technology.Conversely,this review deeply considers the unique value of FPM technology in potentially feeding back to the development of“AI+optics”,such as providing AI benchmark tests under physical constraints,inspirations for the balance of computing power and bandwidth in miniaturized intelligent microscopes,and photoelectric hybrid architectures.Finally,it introduces the industrialization path and frontier directions of FPM technology,pointing out that with the promotion of the dual drive of AI and physics,it will generate a large number of industrial application case,and looks forward to the possibilities of future application scenarios and expansions,for instance,body fluid biopsy and point-of-care testing at the grassroots level represent the expansion of the growth market.
