The evolution of modern sensors for image acquisition brings as much obstacles as many possibilities to obtain multidimensional data with high resolution and rich information. One of the most perceptible destructive factors in visual data is noise. Due to complexity of modern sensors and approaches to signal collecting or preprocessing, noise model becomes complicated. The article’s goal is to introduce and solve a problem of suppressing additive spatially correlated noise (ASCN) which is present in images due to different sources and has various levels of correlation. It is shown that even modern filters attempting to suppress correlated noise often demonstrate unsatisfactory efficiency. Here we propose and analyze two modifications of 2D discrete cosine transform (DCT) based filter and the state-of-the-art BM3D technique. Both are based on accounting spatial spectrum of the noise by setting frequency-dependent thresholds. Furthermore, the modified BM3D filter exploits a similarity measure robust to noise spectrum in block matching.