Redundant Lifted Fast Wavelet Transform for Signal Compression

Lifting wavelet is regarded as the second generation wavelet due to its specific priorities, such as custom-design properties, in-place computation, etc. lifted fast wavelet transform (LFWT) is capable for signal compression, but it is sensitive to signal shift as well as the classical fast wavelet transform (FWT). To LFWT, different circulant shift on the original signal always results in the different compression ratio. Therefore, the optimal shift selection on the original signal can obtain a good compression performance compared with the original signal. This paper introduces redundant strategy into the LFWT, and proposes the redundant LFWT (RLFWT) for exploring all the shift possibility of the original signal to achieve the highest compression ratio by only doubling the computation cost compared with LFWT. Entropy based cost function is employed to obtain the optimal LFWT decomposition and shift step for signal compression. Experiments show that the RLFWT is powerful and effective in signal compression