The objective of this work is to reconstruct high quality gray-level images from bi-level halftone images. We develop optimal inverse halftoning methods for several commonly used halftone techniques, which include dispersed-dot ordered dither, clustered-dot ordered dither, and error diffusion. At first, the least-mean-square (LMS) adaptive filtering algorithm is applied in the training of inverse halftone filters and the optimal mask shapes are computed for various halftone techniques. In the next step, we further reduce the computational complexity by using lookup tables designed by the minimum mean square error (MMSE) method. The optimal masks obtained from the LMS method are used as the default filter masks. Finally, we propose the enhanced MMSE inverse halftone algorithm. It normally uses the MMSE table lookup method for its fast speed. When an empty cell is referred, the LMS method is used to reconstruct the gray-level value. Consequently, the proposed method has the advantages of both excellent reconstructed quality and fast speed. In the experiments, the error diffusion yields the best reconstruction quality among all three halftone techniques.