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Lossless DNA Microarray Image Compression. Source: Thirty-Seventh Asilomar Conference on Signals, Systems and Computers, Vol. 2, Nov. 2003, pp. 1501-1504 Authors: N. Faramarzpour, S. Shirani and J. Bondy Speaker: Chia-Chun Wu ( 吳佳駿 ) Date: 2005/05/13. Outline. - PowerPoint PPT Presentation
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1
Lossless DNA Microarray Image Compression
Source: Thirty-Seventh Asilomar Conference on Signals, Systems and Computers,
Vol. 2, Nov. 2003, pp. 1501-1504 Authors: N. Faramarzpour, S. Shirani
and J. Bondy Speaker: Chia-Chun Wu (吳佳駿 ) Date: 2005/05/13
2
Outline
1. Introduction 2. Spiral path 3. Proposed method 4. Experimental results 5. Conclusions 6. Comments
3
1. Introduction
Microarray images are usually massive in size. about 30MBytes or more
They propose the new concept of spiral path which is an innovative tool for spatial
scanning of images
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2. Spiral path
The idea is to convert the 2D structure of an image into a 1D sequence which can scan the image in a highly
correlated manner while preserving its spatial continuity
It can be used for spatial scanning of any image it is more useful for images with
circular, or central behavior
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2. Spiral path
Spiral path (a) spiral sequence (b) and its differential sequence (c)
(a) (b) (c)
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2. Spiral path
Table Ⅰ
Matrix P for An 18 × 19 Image
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3. Proposed method
Extract individual spots
Calculated initial center coordinates
Divide the sequences
Encode
Input image
Compressed files
NoLast spot?
Tune the spiral path
Yes
16 × 16
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3.1 Spot extraction
0
500
1000
1500
2000
2500
3000
3500
4000
4500
1 9 17 25 33 41 49 57 65
Index
IntX
0
1000
2000
3000
4000
5000
6000
1 9 17 25 33 41 49 57 65
Index
IntY
where Im[i, j] is the image pixel value.
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3.1 Spot extraction
White lines show how spot sub-images are extracted.
spot sub-image
(16 x 16)
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3.1 Spot extraction
spot sub-image
(16 x 16)
mSub= 16, nSub = 16
14 14 15 17 15 16 16 15 15 14 16 18 18 16 16 14 116 15 15 17 17 18 18 22 25 24 22 19 16 12 17 13 219 18 17 19 24 28 35 42 47 44 39 32 24 18 18 17 320 18 21 25 34 43 56 60 64 64 57 49 39 31 20 19 417 19 24 34 49 59 63 65 65 64 63 59 49 40 18 16 517 20 31 46 61 70 64 63 61 62 64 63 56 48 17 15 618 25 39 53 63 68 65 64 64 62 64 64 59 54 17 14 718 27 42 53 59 59 62 63 63 60 60 59 57 52 17 18 820 28 43 56 60 57 60 62 62 60 59 60 59 57 19 17 922 32 47 60 61 56 57 62 63 63 61 60 56 52 18 16 1020 32 49 59 57 51 45 51 59 62 61 61 58 55 15 15 1123 34 49 59 57 50 42 49 56 59 59 59 58 56 18 17 1222 30 45 56 57 54 55 59 62 60 58 57 54 52 19 18 1318 26 37 50 57 57 63 65 64 63 59 58 55 50 17 19 1421 23 32 44 54 58 58 59 60 60 59 57 49 41 21 20 1517 18 22 32 42 47 52 54 56 57 55 49 37 26 17 16 161 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
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3.2 Spiral path fitting
where mSub and nSub are the size of extracted spot sub-image.
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3.2 Spiral path fitting
CenterX = (302×1+379×2+…+
284×15+264×16)/
(302+379+…+
284+264)
=89916/10509= 9
Centery = 97214/10509= 9
(9, 9)
14 14 15 17 15 16 16 15 15 14 16 18 18 16 16 14 1249
16 15 15 17 17 18 18 22 25 24 22 19 16 12 17 13 2286
19 18 17 19 24 28 35 42 47 44 39 32 24 18 18 17 3441
20 18 21 25 34 43 56 60 64 64 57 49 39 31 20 19 4620
17 19 24 34 49 59 63 65 65 64 63 59 49 40 18 16 5704
17 20 31 46 61 70 64 63 61 62 64 63 56 48 17 15 6758
18 25 39 53 63 68 65 64 64 62 64 64 59 54 17 14 7793
18 27 42 53 59 59 62 63 63 60 60 59 57 52 17 18 8769
20 28 43 56 60 57 60 62 62 60 59 60 59 57 19 17 9779
22 32 47 60 61 56 57 62 63 63 61 60 56 52 18 16 10786
20 32 49 59 57 51 45 51 59 62 61 61 58 55 15 15 11750
23 34 49 59 57 50 42 49 56 59 59 59 58 56 18 17 12745
22 30 45 56 57 54 55 59 62 60 58 57 54 52 19 18 13758
18 26 37 50 57 57 63 65 64 63 59 58 55 50 17 19 14758
21 23 32 44 54 58 58 59 60 60 59 57 49 41 21 20 15716
17 18 22 32 42 47 52 54 56 57 55 49 37 26 17 16 16598
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 302
379
528
680
767
791
811
855
886878
856
824
744
660
284
264
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3.2 Spiral path fitting
Spiral path
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3.3 Pixel prediction
where yi s being their pixel values, ri s being their distances from center and nNeighbor is the number of (yi, ri) pairs.
and use ŷ to predict the intensity of our pixel based on r0, its distance to center. In (3) we have
The linear interpolation function:
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3.3 Pixel prediction
Linear interpolation function for 5 neighbors used to predict intensity of the pixel with distance r0 from the center
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3.4 Sequence coding
First, we have a residual sequence with the length mSub×nSub-1 for a mSub×nSub spot sub-image.
Spot parts and background parts of all spot sub-images of the microarray image are concatenated to form two files.
Last, the adaptive Huffman coding is chosen for this application.
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3.4 Sequence coding
Spiral path sequence (a) and prediction residual sequence (b)
(a) (b)
Spot parts Background parts
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3.4 Sequence coding
Spot part (c) and background part (d) of residual sequence
(c) (d)
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4.1 Experimental results
Table Ⅱ
Cumulative Compressed Size of Original File (in Bytes)
Original HeaderSpot reg. Background reg.
Comp-ressed
Original Coded Original Coded
187,702
1,44059,46
242,798
126,922
44,056
88,294
Header: spiral path centers, and first pixel intensity values
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4.2 Experimental results
Table Ⅲ
Compression Ratio of Our Method Compared to Some Others
Method Comp. ratio Method Comp. ratio
GIF 1.54:1 Lossless-4 1.60:1
ZIP 1.67:1 Lossless-5 1.70:1
JPEG-2000 1.74:1 Lossless-6 1.69:1
Lossless-1 1.73:1 Lossless-7 1.79:1
Lossless-2 1.71:1 JPEG-LS 2.02:1
Lossless-3 1.64:1 Our 2.13:1
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5. Conclusions
This paper proposed a lossless compression algorithm for microarray images.
Spiral path and linear neighbor prediction are some of the new concepts proposed in this work.
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6. Comments
從實驗結果可以明顯的發現, Spot區域的壓縮率相較於背景區域而言非常的低,因此可以針對 Spot區域找到一個更適合的壓縮方法,以提昇整體的壓縮率。
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