Word Length Allocation for Multiplier Coefficients of Minimum Lifting Non-Separable 2D Wavelet Transform

Abstract

Ever since the international standard JPEG 2000 based on the lifting wavelet transform was adopted as a core technology of the digital cinema applications, its implementation issues have been discussed from various respects such as memory band width, low latency, high throughput, parallel processing and so on. Unlike the separable two-dimensional (2D) structure of the conventional lifting wavelet transform, the non-separable 2D structure can minimize the total number of lifting steps. It reduces latency of the transform on a parallel signal processing platform at the cost of introducing 2D memory accessing. However, when the word length of coefficient values inside the transform are shortened, the non-separable 2D structure has a problem that its output signal is heavily damaged by the truncation of the coefficient values. Especially, a few coefficients are extremely sensitive to the truncation in this structure. Therefore a careful treatment is required to these sensitive coefficients. In this paper, after investigating the sensitivity of each of the coefficients, a tolerable truncation error is optimally allocated to each coefficient based on the measured sensitivity. As a result, a cost function of the total word length of the wavelet transform is reduced maintaining the total amount of the noise due to truncating the coefficient values. The method is applied to expressing the coefficient values in the sum-of-power-of-two (SPT) format for a low computational load implementation.