Wavelet News

David Barina Wavelet News April 21, 2015 1 / 15

Discrete Wavelet Transform

David Barina Wavelet News April 21, 2015 2 / 15

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

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

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

2-D Discrete Wavelet Transform

David Barina Wavelet News April 21, 2015 6 / 15

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 = UVβ PV

α UHβ P

Hα x

David Barina Wavelet News April 21, 2015 7 / 15

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

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 = MVα,βM

Hα,βx

David Barina Wavelet News April 21, 2015 9 / 15

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

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

2-D Lifting Scheme: Summary

description latency buffer MACs crit. path

CDF 5/3 sep. 4 8 16 2CDF 5/3 sep. new 2 8 28 2CDF 5/3 non-sep. new 3 8 22 4CDF 5/3 non-sep. new 2 8 22 4

David Barina Wavelet News April 21, 2015 12 / 15

FPGA Implementation

MHα,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

MVα,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

3-D Discrete Wavelet Transform

x

y

z

buffer x

buffer y

buffer z

David Barina Wavelet News April 21, 2015 14 / 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