Enhanced temporal and spatial resolution in super-resolution covariance imaging algorithm with deconvolution optimization

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 2n-fold resolution improvement, which can be enhanced to 2(n) 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.

Automated summary

A new SOFI algorithm is proposed in this study, which calculates n orders covariance for each pixel to achieve almost 2n-fold resolution improvement. An optimized deconvolution method is also introduced to further enhance the resolution and suppress noise generation. The algorithm successfully increases the temporal-spatial resolution of SOFI, while preserving the sample's structure, achieving a resolution of 58 nm for 20 experimental images with an acquisition time of 0.8 seconds.