Noise in an image degrades image quality and deteriorates coding efficiency. Recently, various edge-preserving noise filtering methods based on the nonstationary image model have been proposed to overcome this problem. In most conventional nonstationary image models, however, pixels are assumed to be uncorrelated to each other in order not to Increase the computational burden too much. As a result, some detailed information is lost in the filtered results. In this paper, we propose a computationally feasible adaptive noise smoothing algorithm which considers the nonstationary correlation characteristics of images. We assume that an image has a nonstationary mean and can be segmented into subimages which have individually different stationary correlations. Taking advantage of the special structure of the covariance matrix that results from the proposed image model, we derive a computationally efficient FFT-based adaptive linear minimum mean-square-error filter. Justification for the proposed image model is presented and effectiveness of the proposed algorithm is demonstrated experimentally.