In this paper, we propose two new spatially adaptive image fusion algorithms based on Bayesian approach for merging remotely sensed panchromatic and multi-spectral images. The two complementary images are modeled as correlated two dimensional stochastic signals and the high-resolution multi-spectral image is estimated by minimizing the mean squared error between the original high-resolution image and the estimated image. We assume that the estimator is locally linear and obtain the local linear minimum mean square error (MMSE) estimator for image fusion. Two MMSE image fusion algorithms are derived on different assumptions of the images. If we assume that pixels in the images are uncorrelated with their neighbors, the estimator becomes a point processor which is controlled by an adaptive gain expressed by the ratio of local cross-covariance between the two images and the local variance of the panchromatic image. On the other hand, if we assume that pixels in a small block are considered stationary and correlated with one another, the estimator uses the locally stationary cross-covariance matrix between the two images and auto-covariance matrix of the panchromatic image. For the second algorithm, we take Fast Fourier Transform (FFT) based approach in order to avoid complex matrix computations and achieve a fast algorithm. Experimental results show that the proposed algorithms are superior to conventional algorithms according to visual and quantitative comparisons.