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

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


info


• compression• detection• classification• estimation• tracking

…


info

• based onShannon-Nyquist theory (sample 2x faster than the signal BW)

• wide-band signals require high-rate sampling

• compression• detection• classification• estimation• tracking

…



info

IDFT

signal Fourier coefficients


info

IDFT

digitalmsmnts

signalsampling operator


info

IDFT

digitalmsmnts


• 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)


info

IDFT

digitalmsmnts


digital processingCS-ADCanalogworld

info

IDFT

digitalmsmnts

signal

sampling operator

• Dimensionality reduction (compressive sensing, CS)• Can preserve all information in sparse in• Can recover from


info

IDFT

digitalmsmnts

signal

sampling operator

• Can preserve all information in sparse in• Natural to design “random sampling” systems


info

IDFT

digitalmsmnts

signal

sampling operator

Sampling rate: M = O(K log N)

N = Nyquist BW of K = number of active tones


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

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

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