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compressiveSensing-tutorial-eusipco-aug08-print

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Richard Baraniuk Rice University Compressive Sensing
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Acknowledgements For assistance preparing this presentation Rice DSP group – Petros Boufounos, Volkan Cevher – Mark Davenport, Marco Duarte, Chinmay Hegde, Jason Laska, Shri Sarvotham, … Mike Wakin, University of Michigan – geometry of CS, embeddings Justin Romberg, Georgia Tech – optimization algorithms
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Agenda Introduction to Compressive Sensing (CS) – motivation – basic concepts CS Theoretical Foundation – geometry of sparse and compressible signals – coded acquisition – restricted isometry property (RIP) – signal recovery CS Applications Related concepts and work
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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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Sample / Compress compress transmit/store receive decompress sample sparse / compressible wavelet transform Long-established paradigm for digital data acquisition – uniformly sample data at Nyquist rate compress data
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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?
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