基于行的小波变换及其在图像压缩中的应用

The Line-based Wavelet Transform and Application in Image Compression

由于基于行的小波变换编码是以累进方式来完成列向的小波变换 ,其可在不影响小波变换结果的前提下 ,降低对存储容量的需求 ,为此提出用改进的提升格式进行小波变换来替代原算法中的 Mallat算法 ,以加快算法的执行速度。该提升格式是以三项加法单元的形式实现 ,进而把三项加法单元分成两个两项加法单元 ,以进一步节省存储空间 ,但是 ,对于每个单元 ,却增加了一个乘法运算 ,从而计算量增大了。相对于三项加法单元采用一个模式即可求出一组低通滤波结果和高通滤波结果来说 ,两项加法单元对于低通滤波和高通滤波则由于要采用不同的计算步骤 。

According to the line based wavelet transform algorithm, the column transform is performed progressively, so lower memory is required without affecting the result of wavelet transform and it is suitable for the memory insufficient system very much. In this paper, the improved lifting scheme is used to perform wavelet transform to replace the traditional Mallat method that is used in the original algorithm. The three adder unit is adopted to realize lifting scheme. The in place calculation property of the lifting scheme makes the original data updated directly by the current computation result. So the synchronous buffer and the splitting operation are not necessary any more. At the same time, one three adder unit can be divided into two two adder units so that less memory is required. However, two two adder units need one more multiplication in contrast to one three adder unit. Thus, there is more computation in two two adder units. Furthermore, the three adder uses the same operations for low pass lines and high pass lines while the two adder needs different. This algorithm has been tested and compared with JPEG2000 in items of PSNR and bit rate. Experimental results show that it is memory efficient and excellent in compression performance.