The Sparse FFT: - PowerPoint Presentation

Slide1

The Sparse FFT:From Theory to Practice

Dina KatabiO. Abari, E. Adalsteinsson, A. Adam, F. adib, A. Agarwal, O. C. Andronesi, Arvind, A. Chandrakasan, F. Durand, E. Hamed, H. Hassanieh, P. Indyk, B. Ghazi, E. Price, L. Shi, V. StojanovikSlide2

Ongoing

sFFT

Projects (

B

eyond Theory)

Light Field Photography

Spectrum Sharing

Medical Imaging

GPS

sFFT

ChipSlide3

Spectrum CrisisThe FCC predicts a spectrum crunch starting 2013But at any time, most of the spectrum is unused

Spectrum SharingSense to find unused bands; Use them!How do you capture GHz of spectrum? Seattle January 7, 2013Slide4

Challenges in Sparse GHz AcquisitionGHz sampling is expensive and high-power

Tens of MHz ADC< a dollarLow-power A Few GHz ADCHundreds of dollars 10x more power

Compressive sensing using GHz analog mixing is expensive, and requires heavy computation Slide5

Hash the spectrum

into a few bucketsf

Estimate the large coefficient in each non-empty bucket Recap of sFFT

1- Bucketize 2- Estimate Can ignore empty bucketSlide6

Spectrum Sensing & Decoding with

sFFTBucketizeEstimateSlide7

Spectrum Sensing & Decoding with

sFFTBucketizeEstimateSub-sampling time  Aliasing the frequenciesSlide8

Spectrum Sensing & Decoding with

sFFTHash freqs. using multiple co-prime aliasing filtersSame frequencies don’t collide in two filtersIdentify isolated freq. in one filter and subtract them from the other; and iterate …BucketizeEstimate

Low-speed ADCs, which are cheap and low-powerSlide9

Spectrum Sensing & Decoding with

sFFTEstimate frequency by repeating the bucketization with a time shift ∆TBucketizeEstimate ∆Phase

 Slide10

BigBand: Low-Power GHz ReceiverBuilt a 0.9 GHz receiver using three 50 MHz software radios

First off-the-shelf receiver that captures a sparse signal larger than its own digital bandwidth Slide11

Concurrent Senders Hopping in 0.9 GHz

Number of MHz Senders Randomly Hopping gin in 0.9 GHzSlide12

Realtime GHz Spectrum Sensing

Cambridge, MA January 2013sFFT enables a GHz low-power receiver using only a few MHz ADCs Slide13

Probability of Declaring a Used Frequency as Unused Slide14

Ongoing

sFFT

Projects (

B

eyond Theory)

Light Field Photography

Spectrum Sharing

Medical Imaging

GPS

sFFT

ChipSlide15

Magnetic Resonance SpectroscopyAnalyses the chemical making of a brain voxel

Disease Bio-markersSlide16

ChallengesLong acquisition timepatient is in the machine for 40min to hoursArtifacts due to acquisition window Slide17

Windowing ArtifactsFourier transform of a window is a sinc

(Inverse) Fourier TransformAcquisition Window

 Convolution with a

sinc Slide18

Windowing Artifacts

Convolve

Convolve

Discretization

DiscretizationTailSlide19

Challenges with In-Vivo Brain MRSclutter due to

sinc tailhours in machine

Can sparse recovery help?Slide20

Compressive Sensing + 30% dataLost some BiomarkersSlide21

Non-Integer Sparse FFTProblem and ModelSparse in the continuous caseThe railings are because of non-integer frequencies

AlgorithmUse original sparse FFT to estimate integer frequenciesUse gradient descent algorithm to find the non-integer frequencies to minimize the residue of our estimation over the samplesSlide22

Challenges with In-Vivo Brain MRSclutter due to

sinc tailhours in machine

Can sparse recovery help?Slide23

Sparse FFT + 30% of dataRemoved Clutter without losing Biomarkers

sFFT provides clearer images while reducing the acquisition time by 3xSlide24

Light-Field PhotographyGenerate depth and perspective using images from a 2D camera array

Images are correlated 4D frequencies are sparseGoal: Same performance but with fewer imagesSlide25

Original

Reconstructed

with 11

% of dataSlide26

Conclusion Many applications are sparse in the frequency domain and hence can benefit from sFFT

We showed that sFFT enables GHz low-power spectrum sensing and decoding, and improves MRS medical imaging and 4D light-filed captureWe just scratched the surface and expect more applications soon