Compressive Sensing for Multimedia Communications in Wireless Sensor Networks By: Wael BarakatRabih Saliba EE381K-14 MDDSP Literary Survey Presentation March 4 th, 2008

2 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? Sample Compress x N K Transmit/Store N > K Transform Encoder

3 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.

4 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) Key Paper #1

5 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]

6 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! Key Paper #2

7 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. Original 10% 20% [Wakin et al., 2006]

8 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 Key Paper #3

9 Distributed CS Each sensor acquires a signal and performs M j 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.

10 Distributed CS Advantages:  Simple, universal encoding,  Robustness, progressivity and resilience,  Security,  Fault tolerance and anomaly detection,  Anti-symmetrical.

11 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

12 References E. Candès, “Compressive Sampling,” Proc. International Congress of Mathematics, Madrid, Spain, Aug. 2006, pp Baraniuk, R.G., "Compressive Sensing [Lecture Notes]," IEEE Signal Processing Magazine, vol. 24, no. 4, pp , July 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 R. Baraniuk, J. Romberg, and M. Wakin, “Tutorial on Compressive Sensing”, 2008 Information Theory and Applications Workshop, San Diego, California, February 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 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].