Statistical analysis techniques based on auto- and cross-correlations/cumulants, of image stacks of fluctuating objects are used to improve resolution beyond the classical diffraction limit and to reduce the background. The time trajectory of every pixel in the image frame is correlated with itself and/or with the time trajectory of an adjacent pixel. The amplitude of these auto- or cross-correlations/cumulants of each pixel, at a given time lag or averaged or integrated over an interval of time lags, is used as the intensity value of that pixel in the generated superresolved optical fluctuation image.