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Wavelet News

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A single-loop core approach to wavelet lifting.

Published in: Science
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Wavelet News

  1. 1. Wavelet News David Barina Wavelet News April 21, 2015 1 / 15
  2. 2. Discrete Wavelet Transform David Barina Wavelet News April 21, 2015 2 / 15
  3. 3. Lifting Scheme s (0) m = x2m d (0) m = x2m+1 d (1) l = d (0) l + α(s (0) l−1 + s (0) l ) s (1) l−1 = s (0) l−1 + β(d (1) l−1 + d (1) l ) y = UβPαx David Barina Wavelet News April 21, 2015 3 / 15
  4. 4. Lifting Scheme: Latency 2 s(0)d(0)s(0) d(0) s(0) d(0) s(0) d(0) s(1) d(1) s(1) d(1) s(1) d(1)s(1) d(1) y = UβPαx David Barina Wavelet News April 21, 2015 4 / 15
  5. 5. Lifting Scheme: Latency 1 s(0) d(0) s(0) d(0) s(0) d(0)d(0)s(0) s(2) d(1) s(2) d(1) s(2) d(1)s(2) d(1) s(1) y = Mα,βx David Barina Wavelet News April 21, 2015 5 / 15
  6. 6. 2-D Discrete Wavelet Transform David Barina Wavelet News April 21, 2015 6 / 15
  7. 7. 2-D Lifting Scheme a (0) m,n = x2m,2n v (0) m,n = x2m,2n+1 h (0) m,n = x2m+1,2n d (0) m,n = x2m+1,2n+1 y = UV β PV α UH β PH α x David Barina Wavelet News April 21, 2015 7 / 15
  8. 8. 2-D Lifting Scheme: Latency 4, 16 MACs a d h v a d h v a d h v a d h v a d h v a d h v a d h v a d h v a d h v a d h v a d h v a d h v a d h v a d h v a d h v a d h v David Barina Wavelet News April 21, 2015 8 / 15
  9. 9. 2-D Lifting Scheme: Latency 2, 28 MACs a d h v a d h v a d h v a d h v a d h v a d h v a d h v a d h v y = MV α,βMH α,βx David Barina Wavelet News April 21, 2015 9 / 15
  10. 10. 2-D Lifting Scheme: Latency 3, 22 MACs d v h a d v h a d v h a d v h a d v h a d v h a d v h a d v h a d v h a d v h a d v h a d v h a y = AβTα,βDαx David Barina Wavelet News April 21, 2015 10 / 15
  11. 11. 2-D Lifting Scheme: Latency 2, 22 MACs d v h a d v h a d v h a d v h a d v h a d v h a d v h a d v h a d v h a d v h a d v h a d v h a y = AβDαx David Barina Wavelet News April 21, 2015 11 / 15
  12. 12. 2-D Lifting Scheme: Summary description latency buffer MACs crit. path CDF 5/3 sep. 4 8 16 2 CDF 5/3 sep. new 2 8 28 2 CDF 5/3 non-sep. new 3 8 22 4 CDF 5/3 non-sep. new 2 8 22 4 David Barina Wavelet News April 21, 2015 12 / 15
  13. 13. FPGA Implementation MH α,β d (0) m,n a (0) m,n v (0) m,n h (0) m,n d (0) m,n a (1) m,n h (1) m,n d (1) m,n a (1) m−1,n a (2) m−1,n v (2) m−1,n MV α,β d (1) m,n h (1) m,n d (2) m,n a (2) m−1,n v (2) m−1,n a (3) m−1,n v (3) m−1,n a (3) m−1,n−1 a (4) m−1,n−1 h (3) m,n−1 d (2) m,n v (3) m−1,n a (4) m−1,n−1 h (3) m,n−1 BRAM[m] h (2) m,n h (1) m,n a (2) m−1,n h (2) m,n−1 a (2) m−1,n−1 h (1) m,n−1 v (1) m,n a (0) m,n v (0) m,n a (0) m−1,n v (0) m−1,n v (1) m−1,n a (0) m,n v (0) m,n h (0) m,n a (3) m−1,n−1 h (2) m,n−1 a (2) m−1,n−1 h (1) m,n−1 a (3) m−1,n h (2) m,n a (2) m−1,n h (1) m,n DDR[m,n]DDR[m,n] David Barina Wavelet News April 21, 2015 13 / 15
  14. 14. 3-D Discrete Wavelet Transform x y z buffer x buffer y buffer z David Barina Wavelet News April 21, 2015 14 / 15
  15. 15. Future Work streaming unit: multiscale decomposition DWT @ FPGA (Musil et al.) DWT @ GPU (M. Kula) David Barina Wavelet News April 21, 2015 15 / 15

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