cs-tutorial-ITA-feb08-complete

cs-tutorial-ITA-feb08-complete - Richard Baraniuk Rice...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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] – K-sparse 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, x-ray, 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 • Long-established paradigm for digital data acquisition – uniformly sample data at Nyquist rate (2x Fourier bandwidth) sample too much data! 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 Sparsity / Compressibility pixels large wavelet coefficients wideband signal samples large Gabor coefficients time frequency 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 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 Compressive Sensing...
View Full Document

Page1 / 193

cs-tutorial-ITA-feb08-complete - Richard Baraniuk Rice...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online