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The VLSI Design for The VLSI Design for Discrete Wavelet Discrete Wavelet
TransformTransform
The VLSI Design for The VLSI Design for Discrete Wavelet Discrete Wavelet
TransformTransform
微電子電路系微電子電路系 : : 宋志雲 博士宋志雲 博士
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Haar 離散小波轉換
第一次垂直分割程序圖
第一次水平切割程序圖
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原始影像I的四點資料(0,0),(0,1),(1,0),(1,1),經過一階 離散小波轉換後,分別為四個頻率係數所記錄。
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二維三階離散小波轉換示意圖
三階離散小波轉換結果示意圖
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傳統濾波器離散小波轉換• 濾波器的長度 (Filter Tap) 為 4
其中 hm 代表低通濾波器的係數, g m 代表高通濾波器的係數
• 傳統濾波器正、反轉換架構圖
離散小波轉換之正轉換架構
離散小波轉換之反轉換架構
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Living-based
Lifting-based 離散小波轉換架構
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Splitting 模組 :
Lifting 模組:
Scaling 模組:
Xodd(n)=X(2n+1) Xeven(n)=X(2n)
HPF1(n)= Xodd(n)-P(Xeven(n))
LPF1(n)= Xeven(n)+U(HPF1(n))
HPF(n)= K1×HPF1(n)
LPF(n)= K0×LPF1(n)
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Lifting-based 離散小波反轉換
Lifting-based 離散小波反轉換架構
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Lifting algorithm for the 5/3 wavelet
• The analysis filter can be factorized as follow :
where α= - 1/2 , β=1/4
• Architecture for multi-level decomposition MEM
HF VFO1
O2
/ LLHL/ LHHHO3
O4
1)1(
01
10
)1(1)(
1
z
zzP
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Lifting –Based of 5/3 Filter Architecture
HH(i,j)
HL(i,j)
Z
a
H(i,j)
L(i,j)
LH(i,j)
LL(i,j)
+
×
+
+
×
+
ß +
×+
+
a
+
×+
+
×+
L(2i,j)
L(2i+1,j)
H(2i,j)
H(2i+1,j)
x(i,2j+1)
x(i,2j) a
Z
Z
ß
ß
×+Z
-1
Z-1
Z-1
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1-D 9/7 Wavelet Filters• The analysis filter can be factorized as follow :
where α,β,γ,δare the lifting coefficients,ζand 1/ζare scale normalization factors where α = -1.586134342 β = -0.05298011854 γ = 0.829110762 δ = 0.4435068522 ζ = 1.149604389
1 1~ 1 0 1 0 01 (1 ) 1 (1 )
(1 ) 1 (1 ) 1 0 1/0 1 0 1
z zP
z z
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Lifting –Based of 9/7 Filter Architecture
1P 2P1U 2USplit
2USplit
2P1U 2USplit
+
+ +
1U1P
+ +
+
2P
1P
++
++
++ ζ1/
ζ
ζ
ζ1/
ζ
ζ1/
x(i,j)
H1(i,j) H2(i,j)
L1(i,j) L2(i,j)L(i,j)
H(i,j)
LL1(i,j) LL2(i,j)
HH2(i,j)HH1(i,j)
HL1(i,j) HL2(i,j)LH1(i,j) LH2(i,j)
HH(i,j)
HL(i,j)
LH(i,j)
LL(i,j)
2-D lifting-based of 9/7 wavelet filters
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• Architecture for 2-D DWT
• Architecture for multi-level decomposition
HF VF SN
DWT
In HF VF SN
RAM
DWT
Out
LLi
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Comparison
硬體資源比較表
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Experiment• 5/3 濾波器架構中的實驗結果
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PSNR(60.22)
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• 9/7 濾波器架構中的實驗結果
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PSNR(89.23)