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Richard Baraniuk
Rice University
Progress in Analog-to-Information Conversion
The Digital Universe
• Size: 281 billion gigabytes generated in 2007digital bits > stars in the universegrowing by a factor of 10 every 5 years > Avogadro’s number (6.02x1023) in 15 years
• Growth fueled by multimedia data audio, images, video, surveillance cameras, sensor nets, …
• In 2007 digital data generated > total storageby 2011, ½ of digital universe will have no home
[Source: IDC Whitepaper “The Diverse and Exploding Digital Universe” March 2008]
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 actionnew ADCs, cameras, imagers, …
Finding patternsbeyond mere sensing to inference on massive data sets
digital processingADCanalogworld
info
Today’s Data Pipeline
digital processingADCanalogworld
info
Today’s Data Pipeline
• compression• detection• classification• estimation• tracking
…
digital processingADCanalogworld
info
• based onShannon-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
digital processingADCanalogworld
info
IDFT
signal Fourier coefficients
digital processingADCanalogworld
info
IDFT
digitalmsmnts
signalsampling operator
digital processingADCanalogworld
info
IDFT
digitalmsmnts
signalsampling operator
• Sampling rate determined by bandwidth of• But in many applications, is sparse
Sparsity
pixels largewaveletcoefficients
(blue = 0)
widebandsignalsamples
largeGabor (TF)coefficients
time
frequency
Sparsity
• Communications: large spectral bandwidth butsmall information rate(spread spectrum)
• Sensor arrays: large number of sensors butsmall 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)
digital processingADCanalogworld
info
IDFT
digitalmsmnts
signalsampling operator
digital processingCS-ADCanalogworld
info
IDFT
digitalmsmnts
signal
sampling operator
• Dimensionality reduction (compressive sensing, CS)• Can preserve all information in sparse in• Can recover from
digital processingCS-ADCanalogworld
info
IDFT
digitalmsmnts
signal
sampling operator
• Can preserve all information in sparse in• Natural to design “random sampling” systems
digital processingCS-ADCanalogworld
info
IDFT
digitalmsmnts
signal
sampling operator
Sampling rate: M = O(K log N)
N = Nyquist BW of K = number of active tones
digital processingCS-ADCanalogworld
info
IDFT
digitalmsmnts
signal
sampling operator
Sampling rate: M = O(K log N)
• Reduces demands on:– hardware– processing algorithms
Rice CS Research
CSTheory
CS Hardware
CS-basedsignal
processing
Rice CS Research
CSTheory
CS Hardware
CS signalprocessing
• 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
CS Hardware: Single-Pixel Camera
randompattern onDMD array
DMD DMD
single photon detector
imagereconstruction
orprocessing
w/ Kevin Kelly
scene
First Image Acquisition
target 65536 pixels
1300 measurements (2%)
11000 measurements (16%)
CS Hyperspectral Imager
spectrometer
hyperspectral data cube450-850nm
1M space x wavelength voxels200k random sums
CS Hardware: A2I Converter
• UWB ADC based on UWB radio receiver
20MHz sampling rate 1MHz sampling rate
conventional ADC CS-based AIC
HPCT Surveillance via A2I
FMMSKOOK
• 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
HPCT Surveillance via A2I
FMMSKOOK
• Current solution: Rogue system from Applied Signal Technology– bulky, complicated
• Our goal: Rogue performance w/ 30x smaller SWAP
Rice CS Research
CSTheory
CS Hardware
CS signalprocessing
• 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
CS DSP: Array Processing
• Goal: Localize targetsby fusing measurementsfrom an array of sensors
– collect time signal data requires potentially
high-rate (Nyquist)sampling
– communicate signals to central fusion center potentially large
communicationburden
– solve an optimizationproblem ex: MLE beamformer
Enter ELVIS
• ELVIS: Enhanced Localization Via Incoherence and Sparsity
• Number of targets is typically sparse
• Each sensor needonly acquire and transmit a few CSmeasurements to the fusion center– reduces high
sampling rate– reduces comm
burden
Synthetic Results
ELVIS estimate
Field Data Results: Acoustics
Field example: 5 vehicle convoy, 2 HMMV’s and 3 commercial SUV’s.
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
Quantization
• CS currently predominantly a real-valued theory
• In practice, CS measurements are quantized
• Promising progress on 1-bit CS measurements
target40968-bit
pixels
recovery4096 1-bit
msnts
recovery512 1-bit
msnts
Model-based CS
• Sparse/compressible signal model captures simplistic primary structure
wavelets:natural images
Gabor atoms:chirps/tones
pixels:background subtracted
images
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
Tree-Sparse Signal Recovery
target signal CoSaMP, (MSE=1.12)
L1-minimization(MSE=0.751)
Tree-sparse CoSaMP (MSE=0.037)
N=1024M=80
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/[email protected]
dsp.rice.edu/cs
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
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