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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

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
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









what is compressive sensing
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.
compressive sensing cs

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


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
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]

single pixel imaging

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!
single pixel imaging7




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]

distributed cs

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 cs9
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 cs10
Distributed CS
  • Advantages:
    • Simple, universal encoding,
    • Robustness, progressivity and resilience,
    • Security,
    • Fault tolerance and anomaly detection,
    • Anti-symmetrical.
  • 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
  • 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].