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By averaging over all simulated samples, we derived the mean-squared error as a function of spatial frequency: equation(8) ��(kx,ky)=M��|I(kx,ky)?I?(kx,ky)|2��,where the angular brackets denote averaging over 16 randomly generated samples. The factor M ? in Eq. Doxorubicin order 8 ensures that the error approaches 1 in the limit k?1/��k?1/��. Because the ensemble of samples used for our simulations is isotropically distributed, the error should be a function of the magnitude of the spatial frequency, k��kx2+ky2. We therefore expressed the error as a function of k by resampling in bins of width dk?= 0.8/��: equation(9) ��(k)=����(kx,ky)��k��kx2+ky2Vatalanib (PTK787) 2HCl arrowhead and turning on and off over the course of 6400 frames. The arrowhead arrangement creates a spatially varying fluorophore density, with the highest density occurring near the tip of the arrow where all three lines intersect. In this simulation, the mean separation between simultaneously activated emitters, d, was only ?2.4 times the full width at half-maximum of the optical PSF (that is, d ? 5.7��), so that images of neighboring emitters frequently overlapped. Single-emitter localization using PD-1/PD-L1 tumor a maximum-likelihood procedure ( 5?and?6) results in a blurred sample estimate due to erroneous localizations occurring when nearby fluorophores are simultaneously active ( Fig.?2c). A multiemitter fitting procedure, DAOSTORM ( 12), using techniques originally developed for astronomical data analysis, estimates the locations of nearby point sources with overlapping images.?The resulting sample estimate is sharper than that achieved by single-emitter fitting. Yet this technique also results in a blurry region of erroneous localizations ( Fig.?2?d). DAOSTORM does not make use of frame-to-frame temporal correlations resulting from the sequential activation and deactivation of fluorophores, thereby limiting?the accuracy with which each fluorophore can be localized. Here, we report a computational analysis procedure that uses iterative image deconvolution, rather than single- or multiemitter localization, to estimate a superresolution image from fluorescence microscopy data sets. Our technique, deconSTORM, is based on the classic image deconvolution algorithm first proposed by Richardson and Lucy (15?and?16).