# Wavelet Based Lossless Image Compression

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```					Wavelet Based Lossless
Image Compression

Using Partial SPIHT and
Bit Plane Base Arithmetic Coding

1
Abstract
   Proposing an enhanced lossless image
compression called partial SPIHT
   Based on SPIHT
   Uses thresholds that are based on the frequency
of 1s in each bit plane
   Provides higher lossless compression than SPIHT
   Bit plane based arithmetic coder is used

2
Outline
   Section 1 Introduction

   Section 2 S+P transform and SPIHT algorithm

   Section 3 Partial SPIHT algorithm

   Section 4 Bit plane based arithmetic coder

   Section 5 Experiment results

   Section 6 Conclusion
3
Introduction

4
Introduction
   SPIHT is very attractive to medical imaging
   It is capable of progressive transmission
   It may support ROI
   It is capable of compressing images losslessly as
well as lossy
   The lossless scheme uses S-transform and linear
prediction (S+P filter)
   In some cases, transmitting the least significant
bit will decompress the image

5
Introduction
   Proposing a partial SPIHT scheme
   Uses the frequency of 1s occurred in each bit
plane as a threshold

   If the frequency of 1s > a predetermined threshold
   Departs from the SPHIT mode
   Uses two proposed options instead of SPIHT

   Adaptive arithmetic coder is used which is
modified

6
S+P Transform
and SPIHT

7
S-Transform
   Let s[n] be a 1-D sequence of length N
   The S-Transform decomposes s[n] into two
sequences L[n] an H[n]

8
S-Transform
   The inverse of the S-transform

   Where [X] is the largest integer ≦ X

9
S+P Transform
   Predicts high frequency coefficients from
   The low frequency coefficients
   High frequency component is estimated from the
predictor P[n] as:

   At the decoder, the inverse of the predictor H[n] is
evaluated

10
S+P Transform
   Tree predictors PA, PB and PC

11
Wavelet

12
SPIHT
   Uses spatially oriented tree to describe the
relationship between

   The parents on higher levels

   The children and the grandchildren on the lower
levels

13
SPIHT Algorithm
   Let:
   O(I,j): Set of coordinates of all the offspring of node (I,j)
   D(I,j): Set of coordinates of all descendants of node (I,j)
   H: Set of coordinates of all spatial orientation tree roots
(nodes in the highest pyramid level)
   L(I,j) = D(I,j) – O(I,j)

   Type A is pixels in D(I,j)
   Type B is pixels in L(I,j)
   LIS is a list of the insignificant set
   LIP is a list of the insignificant pixels
   LSP is a list of the significant pixels

14
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16
17
SPIHT
   Is very attractive for lossy compression
   Because it provides a high PSNR at low bit rates
   Compression decreases dramatically
   As the least significant bits are transmitted

   Next section, a new algorithm partial SPIHT
   Uses P1 as a threshold to determine using
   SPIHT
   Other new proposed options
18
Partial SPHIT
Algorithm

19
Partial SPIHT
   Higher the P1 in each bit plane using SPIHT
   The more redundant information are needed to be
transmitted

   Figure 2 illustrates the decomposed Lena
image of each bit plane
   In the least significant bit planes
   There is less spatial correlation
   The bit allocation becomes more random

20
Bit plane of Lena(512x512)

21
Partial SPIHT
   SPIHT is used for some bit planes

   SPIHT is not used for other bit plane

   The partial SPIHT decide as follows:

22
Partial SPIHT
   If (P1 ＜ 0.2)
Use SPHIT;
   Because there are many 0s
   If (0.2 ≦ P1 ＜ 0.3)
Use Option_1;
   There are many 2x2 0s
   If (P1 ≦ 0.3)
Use Option_2;
   Nonzero 2x2 sets dominate

23
Option_1
   Use if 0.2 ≦ P1 ＜ 0.3
   The bit plane is partitioned into 2x2 sets

   If all pixels in 2x2 sets are 0s
   transmit 0

   Otherwise
   transmit 1 followed by the 4 bits in the 2x2 set

24
Option_2
   Used if P1 ≧ 0.3
   Partition the bit plane into 2x2 sets

   Transmit the 4 bits in the 2x2 set
without checking

25
Partial SPIHT
   The highest LL level transmits the sets in a
raster scan (rows then columns)
   In the remaining levels
   All the sets are transmitted in the same level
   before moving to the next level
   Sets in the same location in the different
subbands in the same level must be transmitted
   before moving to the next location in the same level

26
Order of the transmitted sets

27
P-SPIHT Algorithm

28
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30
Analysis
   Option_1
   Bitaverage =

   Option_2
   Bitaverage = 4

   SPIHT
   Bitaverage =

   Option_1=4 when P0=0.707
   SPIHT<Option_1 when P0>0.85
   Choose P0=0.8(P1=0.2)

31
Bit Plane Based
Arithmetic Coder

32
Arithmetic coder
   Arithmetic coder was suggested for use in
SPIHT

   Adaptive arithmetic coder is not very
significant in Partial SPIHT

   Thus, proposing a bit plane based adaptive
arithmetic coder
33
Bit plane based coder
   Resets the frequency of all the symbols to 1
for each bit plane

   Coder and decoder must keep track of when
the new plane is coded

   Bit plane based adaptive arithmetic coder
34
Experiment Results
Partial SPIHT VS SPIHT

35
Comparison
   Table 1 compares the file size of nine compressed
images

   Partial SPIHT provided more compression than
SPIHT to most of the tested images

   Mammogram image has a large background area,
which makes SPIHT superior
   Because the background contains a large number of 0s

36
Comparison

37
Conclusion

38
Conclusion
   Partial SPIHT better than SPIHT for most images

   Partial SPIHT evaluates the Probability at each bit
plane then decides using
   SPIHT
   Option_1
   Option_2

   The threshold values are based on experimental
values
39
Thanks
Bye

40

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