Image expansion plays a very important role in image analysis. Common methods of image expansion, such as the zero-order hold method, may generate a visual mosaic to the expanded image, linear and cubic spline interpolation may blur the image data at peripheral regions. Since infrared images have the characteristics of low contrast and low signal-to-noise ratio (SNR), the expanded images derived from common methods are not satisfactory. As shown in the analysis of the course from images with low resolution to those with high resolution, the expansion of image is found to be an ill-posed inverse problem. An image interpolation algorithm based on MAP estimation under Bayesian framework is proposed in this paper, which can effectively preserve the discontinuities in the original image. Experimental results demonstrate that the expanded images by this method are visually and quantitatively (analyzed by using the criteria of mean squared error (MSE) and mean absolute error (MAE)) superior to the images expanded by common methods of linear interpolation. Even in expansion of infrared images, this method can also give good results. An analysis about choosing regularization parameter α in this algorithm is given.