Address all correspondence to S.K. Abramov E-mail: ask379@mail.ru Problems that occur in blind estimation of spatially correlated noise variance in spectral (DCT) domain are considered. It is shown that estimates of noise variance obtained automatically without image pre-processing are considerably biased for most modern techniques. A way to improve accuracy by preliminary downsampling of images is studied. It is demonstrated that downsampling should be adapted to spatial correlation of the noise. An automatic method to determine downsampling parameters is proposed. It is based on analysis of the fourth moment of DCT coefficients in 8x8 image blocks. Comparative analysis for several modern variance estimation techniques is carried out using simulation results for test images from the database TID2008.