cs-tutorial-ICASSP-mar08 - Compressive Sensing Theory and...

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Petros Boufounos Rice University Justin Romberg Georgia Tech Richard Baraniuk Rice University Compressive Sensing Theory and Applications
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Agenda Introduction to Compressive Sensing (CS) [richb] – motivation – basic concepts CS Theoretical Foundation [justin] – signal sparsity – coded acquisition – convex programming Geometry of CS [petros] – sparse and compressible signals – restricted isometry principle (RIP) – recovery algorithms CS Applications [richb, petros]
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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 analog 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 compress transmit/store receive decompress sample JPEG JPEG2000
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Sparsity / Compressibility pixels large wavelet coefficients (blue = 0) wideband signal samples large Gabor (TF) coefficients time frequency
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What’s Wrong with this Picture? Why go to all the work to acquire N samples only to discard all but K pieces of data? compress transmit/store receive decompress sample sparse / compressible wavelet transform
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What’s Wrong with this Picture? linear processing linear signal model (bandlimited subspace) compress transmit/store receive decompress sample sparse / compressible wavelet transform nonlinear processing nonlinear signal model (union of subspaces)
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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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• Signal is - sparse in basis/dictionary – WLOG assume sparse in space domain Samples sparse signal nonzero entries measurements Sampling
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Compressive Data Acquisition
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