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Pros and Cons of Compressive Sensing

Pros and Cons of Compressive Sensing. Richard Baraniuk Rice University. CS – Pro – More General Models. CS works because random projections preserve the structure of the set of sparse signals Random projections preserve the structure of a wide variety of signal classes. Beyond Sparsity.

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Pros and Cons of Compressive Sensing

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  1. Pros and Cons of CompressiveSensing Richard Baraniuk Rice University

  2. CS – Pro – More General Models • CS works becauserandom projectionspreserve the structureof the set of sparsesignals • Random projections preserve the structureof a wide variety of signal classes

  3. Beyond Sparsity Sparse signal model captures simplistic primary structure pixels: background subtracted images wavelets: natural images Gabor atoms: chirps/tones

  4. Structured Sparsity Sparse signal model captures simplistic primary structure Modern compression/processing algorithms capture richer secondary coefficient structure pixels: background subtracted images wavelets: natural images Gabor atoms: chirps/tones

  5. Wavelet Tree-Sparse Recovery CoSaMP, (RMSE=1.12) target signal N=1024M=80 Tree-sparse CoSaMP (RMSE=0.037) L1-minimization(RMSE=0.751)

  6. CS for Manifolds Theorem: random measurements stably embed anL-dim smooth manifoldwhp [B, Wakin, FOCM’08] preservesdistances betweenpoints on the manifold(extension of CS RIP) Key for det/class/learning

  7. CS – Pro – Measurement Noise • Stable recoverywith additive measurement noise • Noise is added to • Stability: noise only mildly amplified in recovered signal

  8. CS – Con – Signal Noise • Often seek recoverywith additive signal noise • Noise is added to • Noise folding: signal noise amplified in by 3dB for every doubling of

  9. CS – Con – Noise Folding

  10. CS – Pro – Dynamic Range • As amount of subsampling grows, can employa higher-resolution quantizer in CS ADC • Thus dynamic range of CS ADC can exceedNyquist ADC • With today’s ADCs, dynamic range gain can exceed5dB for each doubling in

  11. CS – Pro – Dynamic Range

  12. CS – Pro vs. Con

  13. CS – Con – Real-valued Msmnts • Standard CS theory assumes real-valued measurements • Quantization an after-thought • handled as additive measurement noise • Is CS really “compressive”? • impossible to compare the “degree of compression” of CS based on DCT to Nyquist sampling+JPEG compression • Many open problems related to CS and quantization

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