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A new in-band motion compensation algorithm for wavelet-based video coding is proposed: the bottom-up prediction algorithm (BUP). The BUP algorithm overcomes the periodic shift-invariance of the discrete wavelet transform (DWT) and is formalized into new prediction rules using filtering operations. BUP is based on the relationships between the subbands of the shifted input signal and the subbands of the non-shifted reference signal, whereby the number of shifts is limited by the periodic shift-invariance of the DWT. We derive the algorithm for the 1-D DWT with three decomposition levels. The combination of all prediction rules of the BUP algorithm defines a new transform: the bottom-up overcomplete DWT or BUP ODWT, which is shift-invariant. The BUP ODWT calculates the overcomplete subbands by applying the prediction rules to the critically sampled subbands of a wavelet-transformed image. The envisaged application for the BUP algorithm is spatially scalable video coding.