We introduce the bilateral filter BF is the same bilateral filter we use in the HSF for improved resolution synthesis For picture blocks, BR(Bayesian reconstruction) simply uses the conventional JPEG decoder to decode the blocks. RS is a classification based image interpolation scheme which achieves optimal interpolation by training from image pairs at low resolution and high resolution.For At each pixel, HSF uses a locally computed feature vector to predict the relative performance of the filters in estimating the corresponding pixel intensity in the original undistorted image. The prediction result then determines the proportion of each filter used to obtain the final processed output. In this way, the HSF serves as a framework for combining the outputs of a number of different user selected filters, each best suited for a different region of an image. We formulate our scheme in a probabilistic framework where the HSF output is obtained as the Bayesian minimum mean square error estimate of the original image. Maximum likelihood estimates of the model parameters are determined from an offline fully unsupervised training procedure that is derived from the expectation-maximization algorithm. To illustrate how to apply the HSF and to demonstrate its potential, we apply our scheme as a post-processing step to improve the decoding quality of JPEG-encoded document images. The scheme consistently improves the quality of the decoded image over a variety of image content with different characteristics. We show that our scheme results in quantitative improvements over several other state-of-the-art JPEG decoding methods.