Moments reconstruction and local dynamic range compression of high order superresolution optical fluctuation imaging

Cusp-artifacts in high order Superresolution Optical Fluctuation Imaging

“…The point emitters' time blinking trajectories were simulated to blink according to Poisson statistics. Poisson noise was simulated as described in the accompanying manuscript [21]. Actual experimental background noise was recorded using an electron-multiplying charge-coupled device (EMCCD) camera and added to the simulated movie.…”

“…Cusp artifacts are more pronounced for high-order cumulant reconstructions, where the expansion of the dynamic range degrades the quality of the reconstructed image. We used a cusp-artifact-independent method to compress the dynamic range of the pixel intensities (labeled as ldrc; the details are provided in [21]). We compared the obtained results with those of bSOFI reconstructions.…”

“…We also examined and compared a moments-reconstruction approach to cumulants-reconstruction approach. While more details on moments reconstruction are provided in [21], we show here that even-order moments are immune to cusp artifacts and tend to smoothen the features-ofinterest, while still allowing for some degree of resolution enhancement (over the diffraction limit, with the limit being 2 1/2 -fold for the n th -order moment and an additional n 1/2 -fold when deconvolution is performed, resulting in an overall theoretical resolution enhancement of (2n) 1/2 ). Therefore, the proposed method has significant potential for use as a practical (but mathematically nonrigorous) solution for avoiding cusp artifacts.…”

“…Compared to the case for bSOFI, the even-order moments combined with ldrc yield significantly more faithful images up to the 6 th order. (Details are presented in the accompanying manuscript [21]). We showed both theoretically and experimentally that cusp artifacts could be avoided by using even-ordermoment reconstruction [21].…”

“…(Details are presented in the accompanying manuscript [21]). We showed both theoretically and experimentally that cusp artifacts could be avoided by using even-ordermoment reconstruction [21]. With the provided insights about the nature of mixed positive and negative values in the cumulant image, new methods could be developed to decipher the underlying physics through the statistics revealed by the nature of the cumulants by combining multiple orders of cumulants and solve the underlying blinking statistics altogether as a global inverse problem.…”