Lossy Compression of DNA Microarray Images Source: Electrical and Computer Engineering, Vol. 2, May 2004, pp. 735-738 Authors: N. Faramarzpour, S. Shirani and M.J. Deen Speaker: Chia-Chun Wu (吳佳駿) Date: 2005/04/01

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

1. Introduction Microarray images are usually massive in size. about 30MBytes (2560 × 4096) or more Lossless compression is the low compression rate that can be achieved. 2.2:1 in good implementations [4, 5]

Optimize spot coordinates and radius 2. Proposed method Initial radius: (16+16)/2 = 16 Calculated initial spot coordinates and radius Extract individual spots Input image Optimize spot coordinates and radius 16 × 16 Apply Circle to Square (C2S) transform DCT, quantize, and encode Last spot? Yes No Compressed files

where Im[i, j] is the image pixel value. 2.1 Spot extraction where Im[i, j] is the image pixel value.

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

2.1 Spot extraction spot sub-image (16 x 16) msub= 16, nsub = 16 14 15 17 16 18 1 22 25 24 19 12 13 2 28 35 42 47 44 39 32 3 20 21 34 43 56 60 64 57 49 31 4 59 63 65 40 5 46 61 70 62 48 6 53 68 54 7 27 52 8 9 10 51 45 58 55 11 23 50 30 26 37 41 spot sub-image (16 x 16) msub= 16, nsub = 16

2.2 Parameter extraction The initial value for the radius us given by: where γ has a value between 7 and 8, Rp usually converges in 4 or 5 iterations.

2.2 Parameter extraction (9, 9) CenterX = 89916/10509= 9 14 15 17 16 18 1 249 22 25 24 19 12 13 2 286 28 35 42 47 44 39 32 3 441 20 21 34 43 56 60 64 57 49 31 4 620 59 63 65 40 5 704 46 61 70 62 48 6 758 53 68 54 7 793 27 52 8 769 9 779 10 786 51 45 58 55 11 750 23 50 745 30 26 37 41 716 598 302 379 528 680 767 791 811 855 886 878 856 824 744 660 284 264 CenterX = 89916/10509= 9 Centery = 97214/10509= 9 Initial radius Rp=(msub+nsub)/γ = (16+16)/2= 16

2.3 Circle to Square(C2S) transform Geometric representation of C2S transform

2.3 Circle to Square(C2S) transform First, r and Θ are calculated for every pixel belonging to the square. Then we have: where (Xt, Yt) is the center of the square. And then: x is expected to have a value in the range of [0, Rp].

2.3 Circle to Square(C2S) transform 35 36 37 38 39 40 34 41 42 47 44 43 56 60 64 57 49 59 63 65 46 61 70 62 48 53 68 54 50 52 45 51 58 55 14 15 17 16 18 22 25 24 19 12 13 28 35 42 47 44 39 32 20 21 34 43 56 60 64 57 49 31 59 63 65 40 46 61 70 62 48 53 68 54 27 52 51 45 58 55 23 50 30 26 37 41 C2S

2.3 Circle to Square(C2S) transform (a) A microarray image before, and (b) after applying C2S transform to each of its spots.

2.4 DCT, Quantization, and Encoding First, the image is divided into 8 × 8 blocks. Those blocks are then DCT transformed. After DCT is applied to each block, the transformed blocks are quantized. Last, the arithmetic coding is used for this application.

3. Experimental results The rate distortion curve achieved by JPEG compared to lossy compression method for the same test image.

4. Conclusions This paper proposed a new algorithm for lossy compression of microarray images. For various applications which have images with circular patterns, using a stage of C2S transform can provide improvement the overall performance of the compression.

5. Comments 由於DNA Microarray Images背景顏色是不重要的，因此，可以利用本篇論文偵測Spot的方法，將偵測出來的Spot視為重要的ROI區域，以無失真的方式進行壓縮；反之，背景則視為不重要的區域，用失真的方法進行壓縮，以提高整體的壓縮率。