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
The constant in formula (4) is a float-point digital, it is hard to implementation in circuit. By analyzing formula (3) and formula (4) we will found that the constant only lies in large numbers composing low-pass subband, and the calculation is alone ( never effecting neighbor points). We simulated it in Matlab, there is not any vision difference of transformed image between with the constant and without the constant. We omitted the constant in practice.
3 C i r c ui t D e s i g n
3.1 Time analysis
Data inputs one by one every clock. On every start of the lines there is a START with the first data. With START, set the current register odd, and input the first data, next clock, set the current register even, and input the second data. Then every clock the current register changed alternately. So the inputs were subsampled into odds and evens (Figure 2). Input register3 is the delay of input register1, output register3 is the delay of output register1. After some clocks, we can get outputs Y(n) from output register1 and output register2.
We use another sets of registers to processing the first and the last data for boundary extension. This design need not any pre-processing in memory, and need not any logical control in wavelet transform circuit.
3.2 Circuit Architechture
The circuit includes two parts: input output circuit and wavelet transform circuit. Input output circuit includes boundary extending registers and input output control logic, wavelet circuit includes some registers and four adders. Every two adders compose one add node in figure 2. The max time delay lies in adders, pipe-lined adder may contribute higher working frequency. For the coefficients are the power of 2, we use shift and add in stead of multiply, in this way, the hardware source saved and the speed increased.
The synthesized circuit is as same as the design. Figure 3 presents the wavelet transform circuit.
3.3 Simulate Result
The design synthesized on the FPGA Clycone of ALTERA, used 194 LEs, the highest frequency is 200Mhz. Figure 4 presents the result of simulation.
F i na l i ns t r uc t io ns 4
This paper presents a kind of hardware deign on lifting based 5/3 wavelet transform. In this design, the boundary extension is performed while inputting datum, need not any pre-processing on memory, and need not any logic control in wavelet transform circuit, so the circuit is simple. The simulating result shows the design can word well in high frequency.
 I.Daubechies, W. Swendens, Factoring wavelet transforms into liftingsteps, [J], Fourier Ana lysis and Applications, 1998, 4:247 22-69.
 JPEG 2000 Part I Final Committee Draft Version 1.0, [S], 2000
 K. C. B. Tan, Arslan. Low power embedded extensional gorithm for lifting-based discrete wavelet transforming JPEG2000, [J], C. Electronics letters, 2001
胡永生  Uwe Meyer Baese 著？刘凌 译？数字信号处理的FPGA实现, [M], 清华大学出版社？2003
 兰旭光？郑南宁？吴勇？JPEG2000 二维离散小波变换高效并行VLSI 结构设计？[J]？西安交通大学学报？