Compressive Sensing for Multimedia Communications in Wireless Sensor Networks

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Compressive Sensing for Multimedia Communications in Wireless Sensor Networks. EE381K-14 MDDSP Literary Survey Presentation March 4 th , 2008. By: Wael Barakat Rabih Saliba. Introduction to Data Acquisition. Shannon/Nyquist Sampling Theorem

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## Compressive Sensing for Multimedia Communications in Wireless Sensor Networks

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### Compressive Sensing for Multimedia Communications in Wireless Sensor Networks

EE381K-14 MDDSPLiterary Survey Presentation March 4th, 2008

By:Wael Barakat Rabih Saliba

Introduction to Data Acquisition
• Shannon/Nyquist Sampling Theorem
• Must sample more than twice the signal bandwidth,
• Might end up with a huge number of samples  Need to Compress!
• Doing more work than needed?

N > K

K

N

Sample

Transform

Encoder

Transmit/Store

Compress

x

What is Compressive Sensing?
• Combines sampling & compression into one non-adaptive linear measurement process.
• Measure inner products between signal and a set of functions:
• Measurements no longer point samples, but…
• Random sums of samples taken across entire signal.

Key Paper #1

Compressive Sensing (CS)
• Consider an N-length, 1-D, DT signal x in
• Can represent x in terms of a basis of vectors

or

where s is the vector of weighing coefficients and is the basis matrix.

• CS exploits signal sparsity: x is a linear combination of just K basis vectors with K < N (Transform coding)
Compressive Sensing
• Measurement process computes M < N inner products between x and as in . So:
• is a random matrix whose elements are i.i.d Gaussian random variables with zero-mean and 1/N variance.
• Use norm reconstruction to recover sparsest coefficients satisfying such that

[Baraniuk, 2005]

Key Paper #2

Single-Pixel Imaging
• New camera architecture based on Digital Micromirror Devices (DMD) and CS.
• Optically computes random linear measurements of the scene under view.
• Measures inner products between incident light x and 2-D basis functions
• Employs only a single photon detector  Single Pixel!

Original

10%

20%

Single-Pixel Imaging
• Each mirror corresponds to a pixel, can be oriented as1/0.
• To compute CS measurements, set mirror orientations randomly using a pseudo-random number generator.

[Wakin et al., 2006]

Key Paper #3

Distributed CS
• Notion of an ensemble of signals being jointly sparse
• 3 Joint Sparsity Models:
• Signals are sparse and share common component
• Signals are sparse and share same supports
• Signals are not sparse
• Each sensor collects a set of measurements independently
Distributed CS
• Each sensor acquires a signal and performs Mj measurements
• Need a measurement matrix
• Use node ID as a seed for the random generation
• Send measurement, timestamp, index and node ID
• Build measurement matrix at receiver and start reconstructing signal.
Distributed CS
• Simple, universal encoding,
• Robustness, progressivity and resilience,
• Security,
• Fault tolerance and anomaly detection,
• Anti-symmetrical.
Conclusion
• Implement CS on images and explore the quality to complexity tradeoff for different sizes and transforms.
• Further explore other hardware architectures that directly acquire CS data
References
• E. Candès, “Compressive Sampling,” Proc. International Congress of Mathematics, Madrid, Spain, Aug. 2006, pp. 1433-1452.
• Baraniuk, R.G., "Compressive Sensing [Lecture Notes]," IEEE Signal Processing Magazine, vol. 24, no. 4, pp. 118-121, July 2007.
• 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.
• 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].