Earlier techniques used for noise filtering were global filters based on the assumption of a stationary image model. Although the stationarity assumption enables the use of the Fast Fourier transform (FFT)-based algorithm, such filters tend to oversmooth edges where stationarity is not satisfied. Recently, various noise smoothing algorithms 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 a computational burden too much. As a result, some detailed information is lost in the filtered results. We propose a computationally feasible adaptive noise smoothing algorithm that considers the nonstationary correlation characteristics of images. We assume that an image has a nonstationary mean and can be segmented into subimages that 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 for cases of signal uncorrelated additive, multiplicative, and film-grain noises. The justification for the proposed image model is presented, and the effectiveness of the proposed algorithm is demonstrated experimentally.