Fig. 1. (a) Simulated 2D array of ring-like structures with varying radii; (b) wide-field imaging of the simulated ring-like structures; (c) distribution of different SNRs by adding different levels of Poisson noise in a discrete manner along the vertical direction; (d) second-order SOFI of the simulated ring-like structures; (e)–(g) SRRF of the simulated ring-like structures with TRA, TRM, and TRPPM calculation modes; (h)–(j) SRRF of the simulated ring-like structures with TRAC 2, TRAC 3, and TRAC 4 calculation modes; (k) CERN imaging of the simulated ring-like structures; (l) RSP coefficient evaluation of the reconstructed ring-like structures by different imaging methods in the high SNR and low SNR regions; (m)–(p) RSE evaluation of the reconstructed ring-like structures in the low SNR region with TRAC 2, TRAC 3, TRAC 4, and CERN imaging methods. The histograms of (b) and (d) were equalized for clear visualization of the low SNR structures. The source code and data set are available on Github, https://github.com/zhipingzeng/CERN. Scale bar, 500 nm.

Fig. 2. (a) Wide-field image of the simulated tubulin-like network with dynamic doughnut-shaped and point-like nanoscale cargoes moving along network lines; (b), (c) second-order SOFI and SRRF (TRA) images of the simulated dynamic structure; (d) CERN image of the simulated dynamic structure, precisely discerning the doughnut-shaped cargoes (marked by “D”) from the point-like cargoes (marked by “P”); (e)–(h) magnified images indicated by the white dotted regions from (a) to (d). For the cargoes marked by “P,” we generated the cargo images by convolving point-like structures (30 nm radii) with a Gaussian PSF. For the cargoes marked by “D,” we generated the cargo images by convolving ring-like structures (90 nm radii) with a smaller Gaussian PSF. Different PSFs indicated the labeling of two different types of fluorophores with distinct wavelengths for imaging different targets. The blue and red arrows represent the different moving directions of the cargoes along the network lines. Scale bars, 1 μm in (a)–(d); 300 nm in (e)–(h).

Fig. 3. (a), (b) Multicolor wide-field and second-order SOFI images of the subcellular microtubule network and CCPs [33]; (c) SRRF image with TRAC 2 calculation mode of the microtubule network and CCPs; (d) CERN image of the microtubule network and CCPs; (e) line profiles of the wide-field, second SOFI-, SRRF (TRAC 2)-, and CERN-reconstructed CCPs indicated by the white arrows in (f)–(i); (f)–(i) magnified images of the white dotted regions from (a)–(d); (j)–(k) RSE evaluation of the reconstructed CCP in TRAC 2 and CERN imaging; (l) line profiles of the second SOFI-, SRRF (TRAC 2)-, and CERN-reconstructed closely separated filaments located by the red arrows in (b)–(d). Scale bars, 1 μm in (a)–(d); 500 nm in (f)–(i).

Fig. 4. (a) Wide-field image of the densely pack RNA transcripts; (b)–(d) second-order SOFI, SRRF (TRPPM), and SRRF (TRAC 2) images of the RNA molecule distribution; (e) ThunderSTORM image of the RNA molecule distribution [34]; (f) CERN image of the RNA molecules; (g) line profiles of the SRRF (TRPPM)-, SRRF (TRAC 2)-, ThunderSTORM-, and CERN-reconstructed RNA molecules indicated by the white arrows in (c)–(f). (h) FRC comparison of the reconstructed superresolution images from SRRF (TRPPM), SRRF (TRAC 2), ThunderSTORM, and CERN methods. The standard deviations were calculated by using three different image sequences for image reconstructions. Raw data courtesy of the GigaScience Database [34]. Scale bars, 1 μm in (a)–(f).