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

3. 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

4. 4 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

5. 5 2. Spiral path Spiral path (a) spiral sequence (b) and its differential sequence (c) (a) (b) (c)

6. 6 2. Spiral path Table Ⅰ Matrix P for An 18 × 19 Image

7. 7 3. Proposed method Extract individual spots Calculated initial center coordinates Divide the sequences Encode Input image Compressed files No Last spot? Tune the spiral path Yes 16 × 16

8. 8 3.1 Spot extraction where Im[i, j] is the image pixel value.

9. 9 3.1 Spot extraction White lines show how spot sub-images are extracted. spot sub-image (16 x 16)

10. 10 3.1 Spot extraction spot sub-image (16 x 16) m Sub = 16, n Sub = 16 14 15171516 15 141618 16 141 1615 17 18 2225242219161217132 1918171924283542474439322418 173 201821253443566064 5749393120194 1719243449596365 646359494018165 172031466170646361626463564817156 1825395363686564 6264 595417147 1827425359 6263 60 59575217188 2028435660576062 605960595719179 223247606156576263 61605652181610 2032495957514551596261 585515 11 23344959575042495659 5856181712 2230455657545559626058575452191813 1826375057 6365646359585550171914 212332445458 5960 59574941212015 17182232424752545657554937261716 12345678910111213141516

11. 11 3.2 Spiral path fitting where m Sub and n Sub are the size of extracted spot sub- image.

12. 12 3.2 Spiral path fitting Center X = (302×1+379×2+ … + 284×15+264×16)/ (302+379+ … + 284+264) =89916/10509= 9 Center y = 97214/10509= 9 (9, 9) 14 15171516 15 141618 16 141 24 9 1615 17 18 2225242219161217132 28 6 1918171924283542474439322418 173 44 1 201821253443566064 5749393120194 62 0 1719243449596365 646359494018165 70 4 172031466170646361626463564817156 75 8 1825395363686564 6264 595417147 79 3 1827425359 6263 60 59575217188 76 9 2028435660576062 605960595719179 77 9 223247606156576263 61605652181610 78 6 2032495957514551596261 585515 11 75 0 23344959575042495659 5856181712 74 5 2230455657545559626058575452191813 75 8 1826375057 6365646359585550171914 75 8 212332445458 5960 59574941212015 71 6 17182232424752545657554937261716 59 8 12345678910111213141516 30 2 37 9 52 8 68 0 76 7 79 1 81 1 85 5 886 87 8 85 6 82 4 74 4 66 0 28 4 26 4

13. 13 3.2 Spiral path fitting Spiral path

14. 14 3.3 Pixel prediction where y i s being their pixel values, r i s being their distances from center and n Neighbor is the number of (y i, r i ) pairs. and use ŷ to predict the intensity of our pixel based on r 0, its distance to center. In (3) we have The linear interpolation function:

15. 15 3.3 Pixel prediction Linear interpolation function for 5 neighbors used to predict intensity of the pixel with distance r 0 from the center

16. 16 3.4 Sequence coding  First, we have a residual sequence with the length m Sub ×n Sub -1 for a m Sub ×n Sub 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.

17. 17 3.4 Sequence coding Spiral path sequence (a) and prediction residual sequence (b) (a) (b) Spot parts Background parts

18. 18 3.4 Sequence coding Spot part (c) and background part (d) of residual sequence (c) (d)

19. 19 4.1 Experimental results Table Ⅱ Cumulative Compressed Size of Original File (in Bytes) OriginalHeader Spot reg.Background reg. Comp- ressed OriginalCodedOriginalCoded 187,7021,44059,46242,798126,92244,05688,294 Header: spiral path centers, and first pixel intensity values

20. 20 4.2 Experimental results Table Ⅲ Compression Ratio of Our Method Compared to Some Others MethodComp. ratioMethodComp. ratio GIF1.54:1Lossless-41.60:1 ZIP1.67:1Lossless-51.70:1 JPEG-20001.74:1Lossless-61.69:1 Lossless-11.73:1Lossless-71.79:1 Lossless-21.71:1JPEG-LS2.02:1 Lossless-31.64:1Our2.13:1

21. 21 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.

22. 22 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。