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This work presents a class of unidirectional lifting-based wavelet transforms for an arbitrary communication graph in a wireless sensor network. These transforms are unidirectional in the sense that they are computed as data is forwarded towards the sink on a routing tree. We derive a set of conditions under which a lifting transform is unidirectional, then find the full set of those transforms. Among this set, we construct a unidirectional transform that allows nodes to transform their own data using data forwarded to them from their descendants in the tree and data broadcasted to them from their neighbors not in the tree. This provides a higher quality data representation than existing methods for a fixed communication cost.