2. Richard Baraniuk Rice University Progress in Analog-to- Information Conversion

3. The Digital Universe Size: 281 billion gigabytes generated in 2007 digital bits > stars in the universe growing by a factor of 10 every 5 years > Avogadro’s number (6.02x10 23 ) in 15 years Growth fueled by multimedia data audio, images, video, surveillance cameras, sensor nets, … In 2007 digital data generated > total storage by 2011, ½ of digital universe will have no home [Source: IDC Whitepaper “The Diverse and Exploding Digital Universe” March 2008]

4. What’s wrong with today’s data acquisition systems (ADCs)? why go to all the work to acquire massive amounts of sensor data only to throw much/most of it away? A way out: compressive sensing (CS) enables the design of radically new data acquisition systems Compressive sensing in action new ADCs, cameras, imagers, … Finding patterns beyond mere sensing to inference on massive data sets

5. digital processingADC analog world info Today’s Data Pipeline

6. digital processingADC analog world info Today’s Data Pipeline compression detection classification estimation tracking …

7. digital processingADC analog world info based on Shannon-Nyquist theory (sample 2x faster than the signal BW) wide-band signals require high-rate sampling compression detection classification estimation tracking … Today’s Data Pipeline

8. digital processingADC analog world info IDFT signalFourier coefficients

9. digital processingADC analog world info IDFT digital msmnts signal sampling operator

10. digital processingADC analog world info IDFT digital msmnts signal sampling operator Sampling rate determined by bandwidth of But in many applications, is sparse

11. Sparsity pixels large wavelet coefficients (blue = 0) wideband signal samples large Gabor (TF) coefficients time frequency

12. Sparsity Communications:large spectral bandwidth but small information rate (spread spectrum) Sensor arrays:large number of sensors but small number of emitters Wide-field imaging: large surveillance area but small number of targets Key (recent) mathematical fact: Sparse signals support dimensionality reduction (sub-Nyquist sampling)

13. digital processingADC analog world info IDFT digital msmnts signal sampling operator

14. digital processingCS-ADC analog world info IDFT digital msmnts signal sampling operator Dimensionality reduction (compressive sensing, CS) Can preserve all information in sparse in Can recover from

15. digital processingCS-ADC analog world info IDFT digital msmnts signal sampling operator Can preserve all information in sparse in Natural to design “random sampling” systems

16. digital processingCS-ADC analog world info IDFT digital msmnts signal sampling operator Sampling rate: M = O(K log N) N = Nyquist BW of K = number of active tones

17. digital processingCS-ADC analog world info IDFT digital msmnts signal sampling operator Sampling rate: M = O(K log N) Reduces demands on: –hardware –processing algorithms

18. Rice CS Research CS Theory CS Hardware CS-based signal processing

19. Rice CS Research CS Theory CS Hardware CS signal processing DARPA A2I project (with Yehia Massoud, UM, Caltech, AST) Single-pixel camera (with Kevin Kelly) CS-based filtering, detection, classification, estimation, … CS-based array processing Fundamental limits of CS CS with noisy signals Model-based CS

20. CS Hardware: Single-Pixel Camera random pattern on DMD array DMD single photon detector image reconstruction or processing w/ Kevin Kelly scene

21. First Image Acquisition target 65536 pixels 1300 measurements (2%) 11000 measurements (16%)

22. CS Hyperspectral Imager spectrometer hyperspectral data cube 450-850nm 1M space x wavelength voxels 200k random sums

23. CS Hardware: A2I Converter UWB ADC based on UWB radio receiver 20MHz sampling rate1MHz sampling rate conventional ADC CS-based AIC

24. HPCT Surveillance via A2I FM MSK OOK Goal: small, cigarette-pack sized acquisition devices consisting of –radio receiver –A2I converter –simple processor –radio uplink –GPS (space, time) Decode comm signals Geo-locate phones

25. HPCT Surveillance via A2I FM MSK OOK Current solution: Rogue system from Applied Signal Technology –bulky, complicated Our goal: Rogue performance w/ 30x smaller SWAP

26. Rice CS Research CS Theory CS Hardware CS signal processing DARPA A2I project (with Yehia Massoud, UM, Caltech, AST) Single-pixel camera (with Kevin Kelly) CS-based detection, classification, estimation CS-based array processing Fundamental limits of CS CS with noisy signals Model-based CS

27. CS DSP: Array Processing Goal: Localize targets by fusing measurements from an array of sensors –collect time signal data  requires potentially high-rate (Nyquist) sampling –communicate signals to central fusion center  potentially large communication burden –solve an optimization problem  ex: MLE beamformer

28. Enter ELVIS ELVIS: Enhanced Localization Via Incoherence and Sparsity Number of targets is typically sparse Each sensor need only acquire and transmit a few CS measurements to the fusion center –reduces high sampling rate –reduces comm burden

29. Synthetic Results ELVIS estimate

30. Field Data Results: Acoustics Field example: 5 vehicle convoy, 2 HMMV’s and 3 commercial SUV’s.

31. Future Directions CS theory –links between information theory and CS  ex: random projection design via codes –links between machine learning and CS  ex: Johnson-Lindenstrauss lemma –exploiting signal models beyond sparsity –quantization effects and nonlinear CS CS-based signal processing –processing/inference on random projections –matched filter >> smashed filter –multi-signal CS and array processing (improved ELVIS) CS hardware –new A2I architectures for UWB ADC –new camera architectures for wideband imaging

32. Quantization CS currently predominantly a real-valued theory In practice, CS measurements are quantized Promising progress on 1-bit CS measurements target 4096 8-bit pixels recovery 4096 1-bit msnts recovery 512 1-bit msnts

33. Model-based CS Sparse/compressible signal model captures simplistic primary structure wavelets: natural images Gabor atoms: chirps/tones pixels: background subtracted images

34. Model-based CS Sparse/compressible signal model captures simplistic primary structure Modern compression/processing algorithms capture richer secondary coefficient structure wavelets: natural images Gabor atoms: chirps/tones pixels: background subtracted images

35. Tree-Sparse Signal Recovery target signal CoSaMP, (MSE=1.12) L1-minimization (MSE=0.751) Tree-sparse CoSaMP (MSE=0.037) N=1024 M=80

36. CS – Summary Compressive sensing –integrates sensing, compression, processing –exploits signal sparsity information –enables new sensing modalities, architectures, systems Why CS works: stable embedding for signals with concise geometric structure sparse signals | compressible signals | manifolds | … Can perform processing directly on the CS measurements –detection, estimation, filtering, matched filter, … dsp.rice.edu/csrichb@rice.edu

37. dsp.rice.edu/cs

39. ONR talk 20 minutes + questions I follow peter, so he will have some CS background material Audience: Government only (can present proprietary info) Outline: please use existing charts to present the following: –Summary of DARPA A2I funded program: –What is CS and how can it be used to build a better Analog-to- digital converter? –What are implications for metrics? (size, weight, power consumption, SFDR, bandwidth) compared to current art? –How does it work and what is being demonstrated? Future work charts: at your option add any number of charts for any of the following new concepts –Networked CS A2I sensors / convertors for position-location  Play up ELVIS, DCS –Embedded predictive analytics in convertors –Embedded predictive filtering, (Kalman, Weiner, etc.) –How to reduced latency on detection of signals via embedding  Play up CS detection / smashed filter (see markd paper) –investigate networked, position-location, and "predictive / estimation” conversion

40. ONR talk How to pitch –Current designs for ADC, signal processing, etc are based on linear systems and linear subspace models (eg: Nyquist band-limited signals) –Challenge  “real signals” in practical applications live in nonlinear models (this is why we can do compression) –Opportunity  Adapt ADC and processing models to nonlinear models  Can do dimensionality reduction directly on analog data  Promises better hardware, better processing, etc. –CS  Linear acquisition  Nonlinear