Presentation on theme: "The Sparse FFT: From Theory to Practice"— Presentation transcript:
1 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. Stojanovik
3 Spectrum Crisis Spectrum Sharing Sense to find unused bands; Use them! How do you capture GHz of spectrum?The FCC predicts a spectrum crunch starting 2013But at any time, most of the spectrum is unusedSeattle January 7, 2013
4 Challenges in Sparse GHz Acquisition GHz sampling is expensive and high-powerTens of MHz ADC< a dollarLow-powerA Few GHz ADCHundreds of dollars10x more powerCompressive sensing using GHz analog mixing is expensive, and requires heavy computation
5 Recap of sFFT 1- Bucketize 2- Estimate Hash the spectrum into a few buckets Can ignore empty bucket2- EstimateEstimate the large coefficient in each non-empty bucket
6 Spectrum Sensing & Decoding with sFFT BucketizeEstimate
7 Spectrum Sensing & Decoding with sFFT BucketizeEstimateSub-sampling time Aliasing the frequencies
8 Spectrum Sensing & Decoding with sFFT BucketizeEstimateHash 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 …Low-speed ADCs, which are cheap and low-power
9 Spectrum Sensing & Decoding with sFFT BucketizeEstimateEstimate frequency by repeating the bucketization with a time shift ∆T∆Phase =2𝜋𝑓 ∆𝑇
10 BigBand: Low-Power GHz Receiver Built a 0.9 GHz receiver using three 50 MHz software radiosFirst off-the-shelf receiver that captures a sparse signal larger than its own digital bandwidth
11 Concurrent Senders Hopping in 0.9 GHz Number of MHz Senders Randomly Hopping gin in 0.9 GHz
12 Realtime GHz Spectrum Sensing Cambridge, MA January 2013sFFT enables a GHz low-power receiver using only a few MHz ADCs
13 Probability of Declaring a Used Frequency as Unused
19 Challenges with In-Vivo Brain MRS clutter due to sinc tailhours in machineCan sparse recovery help?
20 Compressive Sensing + 30% data Lost some Biomarkers
21 Non-Integer Sparse FFT Problem and ModelSparse in the continuous caseThe railings are because of non-integer frequenciesAlgorithmUse 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 samples
22 Challenges with In-Vivo Brain MRS clutter due to sinc tailhours in machineCan sparse recovery help?
23 sFFT provides clearer images while reducing the acquisition time by 3x Sparse FFT + 30% of dataRemoved Clutter without losing BiomarkerssFFT provides clearer images while reducing the acquisition time by 3x
24 Light-Field Photography Generate depth and perspective using images from a 2D camera arrayImages are correlated 4D frequencies are sparseGoal: Same performance but with fewer images
26 ConclusionMany applications are sparse in the frequency domain and hence can benefit from sFFTWe 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
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