Compressive Sensing for Multimedia Communications in Wireless Sensor

Recall Compressive Sensing (CS) n CS combines acquisition & compression. q q n Measurement,

Framework n n 3 Test Images: Grayscale, n N n M << N Project

Need for Quantization n Measurement vector n Quantize measurements for digital transmission n 2

Peppers – [16 9] Quantization 5, 000 Measurements (7. 6%) 13, 232 Measurements (20.

Peppers – [8 6] Quantization 5, 000 Measurements (7. 6%) 13, 232 Measurements (20.

Barbara – [8 6] Quantization 5, 000 Measurements (7. 6%) 13, 232 Measurements (20.

Lena – [8 6] Quantization 5, 000 Measurements (7. 6%) 13, 232 Measurements (20.

Numerically… n Image size by format: q q q n TIFF: 64 KB JPEG:

References I n n E. Candès, “Compressive Sampling, ” Proc. International Congress of Mathematics,

References II n n n Baraniuk, R. G. , "Compressive Sensing [Lecture Notes], "

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Compressive Sensing for Multimedia Communications in Wireless Sensor Networks EE 381 K-14 MDDSP Literary Survey Presentation March 4 th, 2008 By: Wael Barakat Rabih Saliba

Recall Compressive Sensing (CS) n CS combines acquisition & compression. q q n Measurement, Reconstruction. Objective: examine the benefits of CS when used in wireless sensor networks for imaging purposes. 2

Framework n n 3 Test Images: Grayscale, n N n M << N Project M Q[. ] M Reconstruction N Quality measure: Structural Similarity Index (SSIM) 3

Need for Quantization n Measurement vector n Quantize measurements for digital transmission n 2 float implementations: q q is real-valued [8 6] quantization, [16 9] quantization. [ word_length exponent_length ] (in bits) 4

Peppers – [16 9] Quantization 5, 000 Measurements (7. 6%) 13, 232 Measurements (20. 2%) 21, 866 Measurements (33. 4%) Original 5

Peppers – [8 6] Quantization 5, 000 Measurements (7. 6%) 13, 232 Measurements (20. 2%) 21, 866 Measurements (33. 4%) Original 6

Barbara – [8 6] Quantization 5, 000 Measurements (7. 6%) 13, 232 Measurements (20. 2%) 21, 866 Measurements (33. 4%) Original 7

Lena – [8 6] Quantization 5, 000 Measurements (7. 6%) 13, 232 Measurements (20. 2%) 21, 866 Measurements (33. 4%) Original 8

SSIM - Lena 9

SSIM Comparison 10

Numerically… n Image size by format: q q q n TIFF: 64 KB JPEG: 45. 6 KB (maximum compression) 30% Measurements: 19. 2 KB (with [8 6] quantization) Reduction by 58%! (from JPEG) => in terms of transmitted bits, and => energy consumption at sensor 11

References I n n E. Candès, “Compressive Sampling, ” Proc. International Congress of Mathematics, Madrid, Spain, Aug. 2006, pp. 1433 -1452. M. Duarte, M. Wakin, D. Baron, and R. Buraniak, “Universal Distributed Sensing via Random Projections”, Proc. Int. Conference on Information Processing in Sensor Network, Nashville, Tennessee, April 2006, pp. 177 -185. R. Baraniuk, J. Romberg, and M. Wakin, “Tutorial on Compressive Sensing”, 2008 Information Theory and Applications Workshop, San Diego, California, February 2008. M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly and R. Baraniuk, “An Architecture for Compressive Imaging”, Proc. Int. Conference on Image Processing, Atlanta, Georgia, October 2006, pp. 1273 -1276. 12

References II n n n Baraniuk, R. G. , "Compressive Sensing [Lecture Notes], " IEEE Signal Processing Magazine, vol. 24, no. 4, pp. 118 -121, July 2007. M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly and R. Baraniuk, “Single-Pixel Imaging via Compressive Sampling”, IEEE Signal Processing Magazine [To appear]. Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, "Image quality assessment: From error visibility to structural similarity, " IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600 -612, Apr. 2004. SSIM Code: http: //www. ece. uwaterloo. ca/~z 70 wang/research/ssim/ L 1 -Magic Code & Documentation: http: //www. acm. caltech. edu/l 1 magic/ 13