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A VLSI Architecture for the 2-D Discrete Wavelet Transform

A VLSI Architecture for the 2-D Discrete Wavelet Transform. Zhiyu Liu Xin Zhou May 2004. Motivation. To apply the knowledge learned in ECE734 to practical problems Popular Methods Folding Parallel Pipeline Systolic … Possible Application Image Processing (Discrete Wavelet Transform)

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A VLSI Architecture for the 2-D Discrete Wavelet Transform

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

  5. Mallat’s Pyramid Algorithm y(1,n) HPF 2 y(2,n) x(n) HPF 2 y(3,n) LPF 2 HPF 2 LPF 2 x(1,n) LPF 2 • 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,

  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) 0 Octave1 Row + Octave1 Column 1 Octave2 Row + Octave2 Column 2 Octave1 Row + Octave1 Column 3 Octave3 Row + Octave3 Column 4 Octave1 Row + Octave1 Column 5 Octave2 Row + Octave2 Column 6 Octave1 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

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