Implementation of JPEG2000 Le Call wavelet
Dai wen bo
The School of Information Engineering
WuHan University of Technology
WuHan, HuBei, 430063
This paper presents an approach towards JPEG2000 recommended lifting-based Le
Call 5/3 wavelet transform. The deign performs boundary extending while inputting
datum, and only uses few shifters and adders, the architecture is efficient and height
performance. The deign simulated on FPGA.
Keywords: JPEG2000, wavelet transform, lifting scheme, FPGA
1 Int ro ducti o n
Wavelet transform has a lot of advantages that suit for image compression, such as acceptable performance even at very low bit rates, region of interest coding, lossy and lossless performance using same coder, non-iterative rate control etc. In some cases, hardware implementation of wavelet transform is needed for portable and height performance.
Traditional wavelet transform uses Mallet arithmetic which based-on convolution, it is complex and hard to be implemented on hardware. I. Daubechies and W. Swendens have given an new arithmetic based on lifting scheme which called the second generation wavelet, the new arithmetic have advantages such as in-place implementation of the fast wavelet transform, possibility of intergers to intergers transform, the same complex of forward and inverse transform, it is suit for hardware implementation.
The JPEG2000 recommended Le Call 5/3 wavelet has the coefficient which is the power of 2, and it is a kind of integer to integer transform. In this case, multipliers could be instead by shifters and adders, the source saved markedly.
This paper presents an FPGA implementation of modified lifting-based Le Call 5/3 wavelet transform. The boundary extending is performed while input datum, and only use few shifters and adders to performing computation. The architecture is efficient.
Li ft ing sche m e o f 5/ 3 w av el et tra ns fo rm 2
I. Daubechies and W. Swendens represented the lifting scheme of wavelet transform, the basic idea is factoring wavlet transform into lifting steps, namely, factoring polyphase matrixes into upper triangular matrixes？ lower triangular matrix, and constants. Lifting scheme includes three steps: splitting, predicting, and updating, as represented in figure 1.
Even Smooth Y(2n) +
Split Predict Update
+ Odd Detail Y(2n+1)
Figure 1 : Lifting Steps
Lifting stage is so called lazy transform, which subsamples inputs into odd and even; predicting stage lifts the low-pass subband with the help of high-pass subband; updating stage lifts the high-pass subband with the help of low-pass subband.
Formula (1) and formula (2) represent the lifting scheme of 5/3 wavelet. Xext is the extended signal, Y(2n+1) is the high-pass subband which means details of image, Y(2n) is the low-pass subband which means smooth of image.
Since the actual data in an image transform is finite in length, boundary extension becomes a crucial part of every wavelet decomposition scheme. For symmetrical odd-tap filter (the Le Call 5/3 wavelet is in this category), symmetrical boundary extension can be used. Assuming the original signal is 12345678, then the extended signal is 432 | 12345678 | 765. The length of filter determines the symbols need extending, which means only one symbol need extending in 5/3 wavelet. The extension can be performed before wavelet transform, or at the same time of wavelet transform. The later is so called embedded extension. We use some delay register to extending the boundary.
Figure 2 : Register Relationship