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Unformatted text preview: Richard Baraniuk Rice University Justin Romberg Georgia Tech Michael Wakin University of Michigan Tutorial on Compressive Sensing 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] – Ksparse and compressible signals – manifolds • CS Applications [richb, justin] Compressive Sensing Introduction and Background Digital Revolution 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, xray, gamma ray, … 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? 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 Sensing by Sampling • Longestablished paradigm for digital data acquisition – uniformly sample data at Nyquist rate (2x Fourier bandwidth) sample too much data! Sensing by Sampling • Longestablished paradigm for digital data acquisition – uniformly sample data at Nyquist rate (2x Fourier bandwidth) – compress data (signaldependent, nonlinear) compress transmit/store receive decompress sample sparse wavelet transform Sparsity / Compressibility pixels large wavelet coefficients wideband signal samples large Gabor coefficients time frequency What’s Wrong with this Picture? • Longestablished paradigm for digital data acquisition – sample data at Nyquist rate (2x bandwidth) – compress data (signaldependent, nonlinear) – brick wall to resolution/performance compress transmit/store receive decompress sample sparse / compressible wavelet transform Compressive Sensing (CS) • Recall Shannon/Nyquist theorem – Shannon was a pessimist – 2x oversampling Nyquist rate is a worstcase 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 Compressive Sensing...
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 Spring '10
 RunyiYu
 Signal Processing, Nyquist–Shannon sampling theorem, compressive sensing, Richard Baraniuk

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