Inverse halftoning (IH) is used to reconstruct the gray image from an input halftone image. This paper presents a machine learning-based IH algorithm to reconstruct the high quality gray images. We first propose a novel variance gain-based tree construction approach to build up an approximate decision tree (DT). Based on the constructed DT, a texture- based training process is presented to construct a lookup tree-table which will be used in the reconstructing process. In our implementation, thirty training images are used to build up the lookup tree-table and five popular testing images are used to justify the quality performance of our proposed IH algorithm. Experimental results demonstrate that although our IH algorithm needs longest execution-time, it has the highest image quality when compared to the published three IH algorithms.