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Recently we have proposed a Look Up Table (LUT) based method for inverse halftoning of images. The LUT for inverse halftoning is obtained from the histogram gathered from a few sample halftone images and corresponding original images. The method is extremely fast (no filtering is required) and the image quality achieved is comparable to the best methods known for inverse halftoning. The size of the LUT can become bigger even though most of the elements in the table are not used in practice. We propose a tree structure which will reduce the storage requirements of an LUT by avoiding nonexistent patterns. Tree-structure inverse halftoning will need only a fraction of its LUT equivalent for storage. We demonstrate the performance on error diffused images.