A new scheme of super-resolution optical fluctuation imaging (SOFI) is proposed to broaden its application in the high-order case by separating the elimination of shot noise from the computation of cumulant, applying the low-pass denoising (LPD) operator to SOFI. The high-order cumulants are derived from a basic recursion of moments with the suppression of shot noise by the LPD on raw data. SOFI based on LPD (LPD-SOFI) demonstrates a 10.6-fold lateral resolution enhancement with the cumulant order of the 16th and a seven-fold three-dimensional resolution enhancement with the cumulant order of the 10th in experiments performed on a sparse sample of quantum dots.
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