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Enhanced temporal and spatial resolution in super‐resolution covariance imaging algorithm with deconvolution optimization
Journal of Biophotonics ( IF 2.0 ) Pub Date : 2020-10-27 , DOI: 10.1002/jbio.202000292 Xuehua Wang 1 , Junping Zhong 1 , Mingyi Wang 1 , Honglian Xiong 1 , Dingan Han 1 , Yaguang Zeng 1 , Haiying He 2 , Haishu Tan 1
Journal of Biophotonics ( IF 2.0 ) Pub Date : 2020-10-27 , DOI: 10.1002/jbio.202000292 Xuehua Wang 1 , Junping Zhong 1 , Mingyi Wang 1 , Honglian Xiong 1 , Dingan Han 1 , Yaguang Zeng 1 , Haiying He 2 , Haishu Tan 1
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Based on the numerical analysis that covariance exhibits superior statistical precision than cumulant and variance, a new SOFI algorithm by calculating the n orders covariance for each pixel is presented with an almost 
‐fold resolution improvement, which can be enhanced to 2n via deconvolution. An optimized deconvolution is also proposed by calculating the (n + 1) order SD associated with each n order covariance pixel, and introducing the results into the deconvolution as a damping factor to suppress noise generation. Moreover, a re‐deconvolution of the covariance image with the covariance‐equivalent point spread function is used to further increase the final resolution by above 2‐fold. Simulated and experimental results show that this algorithm can significantly increase the temporal–spatial resolution of SOFI, meanwhile, preserve the sample's structure. Thus, a resolution of 58 nm is achieved for 20 experimental images, and the corresponding acquisition time is 0.8 seconds.
中文翻译：
具有解卷积优化的超分辨率协方差成像算法中增强的时空分辨率
基于数值分析，协方差比累积量和方差表现出更高的统计精度，提出了一种通过计算每个像素的n阶协方差的新SOFI算法，其分辨率提高了近几倍，可以通过反卷积将其提高到2 n。通过计算 与每个n相关的（n +1）阶SD也提出了优化的反卷积阶协方差像素，并将结果引入去卷积作为阻尼因子以抑制噪声的产生。此外，使用协方差等效点扩展函数对协方差图像进行反卷积可将最终分辨率进一步提高2倍以上。仿真和实验结果表明，该算法可以显着提高SOFI的时空分辨率，同时保留样本的结构。因此，对于20个实验图像，实现了58 nm的分辨率，相应的采集时间为0.8秒。
更新日期：2020-10-27
‐fold resolution improvement, which can be enhanced to 2n via deconvolution. An optimized deconvolution is also proposed by calculating the (n + 1) order SD associated with each n order covariance pixel, and introducing the results into the deconvolution as a damping factor to suppress noise generation. Moreover, a re‐deconvolution of the covariance image with the covariance‐equivalent point spread function is used to further increase the final resolution by above 2‐fold. Simulated and experimental results show that this algorithm can significantly increase the temporal–spatial resolution of SOFI, meanwhile, preserve the sample's structure. Thus, a resolution of 58 nm is achieved for 20 experimental images, and the corresponding acquisition time is 0.8 seconds.
中文翻译：
具有解卷积优化的超分辨率协方差成像算法中增强的时空分辨率
基于数值分析，协方差比累积量和方差表现出更高的统计精度，提出了一种通过计算每个像素的n阶协方差的新SOFI算法
，其分辨率提高了近几倍，可以通过反卷积将其提高到2 n。通过计算 与每个n相关的（n +1）阶SD也提出了优化的反卷积阶协方差像素，并将结果引入去卷积作为阻尼因子以抑制噪声的产生。此外，使用协方差等效点扩展函数对协方差图像进行反卷积可将最终分辨率进一步提高2倍以上。仿真和实验结果表明，该算法可以显着提高SOFI的时空分辨率，同时保留样本的结构。因此，对于20个实验图像，实现了58 nm的分辨率，相应的采集时间为0.8秒。
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