Lossless DNA Microarray Image Compression

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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

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Outline

1. Introduction 2. Spiral path 3. Proposed method 4. Experimental results 5. Conclusions 6. Comments

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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。