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Optimum SPT allocation for multipliers of minimum lifting 2D wavelet transform

Implementation issues of the separable 2D lifting wavelet transform has been discussed under the international standard JPEG 2000 scheme. Recently, the minimum lifting step structure of the transform was proposed introducing the multi-dimensional memory accessing. It can reduce latency in a parallel processing platform. However, its output signal is distorted due to truncation of multiplier coefficient values. Especially, a few coefficients are extremely sensitive to the truncation in this structure. Therefore a special treatment is required to these coefficients. In this paper, a tolerable (the maximum) truncation error is optimally assigned to each coefficient under a given cost function introducing the noise gain. It is applied to expressing coefficient values in the sum-of-power-of-two (SPT) format for reducing computational cost of multipliers of the transform.