This paper presents two methods to fuse a low spatial resolution multispectral image and a high spatial resolution panchromatic one to produce a new multispectral image with high spatial resolution. First, the Poisson fusion method is developed based on minimizing the gradient difference between the synthesized image and the panchromatic image with boundary conditions sampled from the multispectral image. The fusion result can therefore be achieved by solving the Poisson equation with Dirichlit boundary conditions. Secondly, an optimal fusion technique, which minimizes the gradient difference and the color difference with respect to the panchromatic and multispectral images respectively is given and the result is induced by an iterative optimization algorithm. Both of them can be applied to color composites and individual bands. Their advantages of the fidelity to spectral property and the spatial resolution improvement over the HSI, Brovey, PCA and wavelet transform are convincingly demonstrated in the experiments from visual evaluation and statistical analysis.