In this paper, we presents a spatially adaptive noise detection and removal algorithm. Under the assumption that an observed image and the additive noise have Gaussian distribution, the noise parameters are estimated with local statistics, and the parameters are used to define the constraints on the noise detection process, where the first order Markov Random Field (MRF) is used. In addition, an adaptive low-pass filter having a variable window sizes defined by the constraints on noise detection is used to control the degree of smoothness of the reconstructed image. Experimental results demonstrate the capability of the proposed algorithm.