Efficient lifting based CDF9/7 wavelet transform using fixed point

Lifting based CDF9/7 wavelet transform is used for lossy coding. As the lifting coefficients are irrational numbers, floating point calculation lead the transform process slow. Using integer numbers instead of float numbers, fixed point calculation have a faster performance. However, where to make the floating point fixed should be determined, because the position of fixed point affects the kept accuracy of lifting coefficients, and then affects the effect of the wavelet transform. In this paper, by changing both the fixed point positions of lifting coefficients “Lifting Coefficients Shift” and the shifted bits of image signal values “Signal Values Shift”, combining with different rounding methods, we compare the quality of images after 6 levels of CDF9/7 forward and inverse wavelet transform, and find out: When the ratio of “Lifting Coefficients Shift” to “Signal Values Shift” is 12:5 with rounding towards +∞, it has the best result for fixed point CDF9/7 wavelet transform. For further validation, we test it by run time and implement of image compression. It has not only a faster performance but also a better quality for image compression.