1. A VLSI Architecture for the 2-D Discrete Wavelet Transform Zhiyu Liu Xin Zhou May 2004

2. Motivation To apply the knowledge learned in ECE734 to practical problems  Popular Methods Folding Parallel Pipeline Systolic …  Possible Application Image Processing (Discrete Wavelet Transform) Speech Processing Communication Systems …

3. Goal To propose a new VLSI architecture to implement 2-D Discrete Wavelet Transform (DWT).  Based on RPA (Recursive Pyramid Algorithm)  Parallel Architecture  Systolic Architecture to Deal with Borders

4. Wavelets: functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale 2 2 Wavelet Transform

5. Mallat’s Pyramid Algorithm Mallat algorithm : Hierarchically perform DWT decomposition and reconstruction. If the coefficients of two scale equation is looked as filter, then mallat algorithm is in reality two-channel filter banks. In the sense, scale function and wavelet are known as low-pass filter and high-pass filter, HPF LPF x(n) 2 2 HPF LPF 2 2 HPF LPF 2 2 y(1,n) y(2,n) y(3,n) x(1,n)

6. Recursive Pyramid Algorithm RPA is a modification of Mallat’s PA In Mallat’s PA, each level is completely computed before the next RPA rearranges the order of the N outputs such that an output is scheduled at the `earliest' instance that it can be scheduled. The earliest instance is based on the following precedence relation: if the earliest `instance' of the ith octave clashes with that of the (i + 1)th octave, then the ith octave gets scheduled first.

7. Recursive Pyramid Algorithm(Cont.)

8. Recursive Pyramid Algorithm(Cont.2)

9. Proposed Algorithm Using Parallel Architecture to build up row- based RPA and using the Systolic Architecture to deal with borders

10. Proposed Algorithm(Cont.) Row based RPA  Intersperse the row operation of various octaves in between the first octave  After each row operation, we proceed the column operation

11. Proposed Algorithm(Cont.1) 0Octave1 Row + Octave1 Column 1Octave2 Row + Octave2 Column 2Octave1 Row + Octave1 Column 3Octave3 Row + Octave3 Column 4Octave1 Row + Octave1 Column 5Octave2 Row + Octave2 Column 6Octave1 Row + Octave1 Column…

12. Proposed Algorithm(Cont.2) --- Hardware Implementation Architecture

13. Proposed Algorithm(Cont.3) -- Dealing with Borders Decomposition of Periodic Extension RPA Reconstruction of Periodic Extension RPA

14. Proposed Algorithm(Cont.4)

15. Conclusion Parallel  To speed up the chip Periodic extension  Implement the perfect reconstruction  Compute coefficients. Future work  Theoretic analysis