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cs-tutorial-ITA-feb08-complete - Tutorial on Compressive...

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Richard Baraniuk Rice University Justin Romberg Georgia Tech Michael Wakin University of Michigan Tutorial on Compressive Sensing
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Agenda Introduction to Compressive Sensing (CS) [richb] – motivation – basic concepts CS Theoretical Foundation [justin] – uniform uncertainty principles – restricted isometry principle – recovery algorithms Geometry of CS [mike] K -sparse and compressible signals – manifolds CS Applications [richb, justin]
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Compressive Sensing Introduction and Background
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Digital Revolution
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Pressure is on Digital Sensors Success of digital data acquisition is placing increasing pressure on signal/image processing hardware and software to support higher resolution / denser sampling » ADCs, cameras, imaging systems, microarrays, … x large numbers of sensors » image data bases, camera arrays, distributed wireless sensor networks, … x increasing numbers of modalities » acoustic, RF, visual, IR, UV, x-ray, gamma ray, …
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Pressure is on Digital Sensors Success of digital data acquisition is placing increasing pressure on signal/image processing hardware and software to support higher resolution / denser sampling » ADCs, cameras, imaging systems, microarrays, … x large numbers of sensors » image data bases, camera arrays, distributed wireless sensor networks, … x increasing numbers of modalities » acoustic, RF, visual, IR, UV = deluge of data deluge of data » how to acquire, store, fuse, process efficiently?
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Digital Data Acquisition • Foundation: Shannon sampling theorem “if you sample densely enough (at the Nyquist rate), you can perfectly reconstruct the original data” time space
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Sensing by Sampling Long-established paradigm for digital data acquisition – uniformly sample data at Nyquist rate (2x Fourier bandwidth) sample too much data!
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Sensing by Sampling Long-established paradigm for digital data acquisition – uniformly sample data at Nyquist rate (2x Fourier bandwidth) compress data (signal-dependent, nonlinear) compress transmit/store receive decompress sample sparse wavelet transform
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Sparsity / Compressibility pixels large wavelet coefficients wideband signal samples large Gabor coefficients time frequency
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What’s Wrong with this Picture? Long-established paradigm for digital data acquisition sample data at Nyquist rate (2x bandwidth) compress data (signal-dependent, nonlinear) brick wall to resolution/performance compress transmit/store receive decompress sample sparse / compressible wavelet transform
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Compressive Sensing (CS) Recall Shannon/Nyquist theorem – Shannon was a pessimist – 2x oversampling Nyquist rate is a worst-case bound for any bandlimited data – sparsity/compressibility irrelevant – Shannon sampling is a linear process while compression is a nonlinear process Compressive sensing – new sampling theory that leverages compressibility – based on new uncertainty principles randomness plays a key role
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Compressive Sensing Directly acquire “ compressed ” data Replace samples by more general “measurements” compressive sensing transmit/store receive reconstruct
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