DCS_Asilomar_Nov2 - Distributed Compressed Sensing Dror...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE Department Rice University dsp.rice.edu Distributed Compressed Sensing Dror Baron Marco Duarte Shriram Sarvotham Michael Wakin Richard Baraniuk
Background image of page 1

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

View Full Document Right Arrow Icon
Distributed Compressed Sensing
Background image of page 2
Signal Representation • Representation (basis, frame) – spikes, Fourier sinusoids, wavelets, etc … • For orthonormal , coefficient = projection (inner product) of x onto basis function
Background image of page 3

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

View Full Document Right Arrow Icon
Sparse Signal Representations • For maximum efficiency , choose representation so that coefficients are sparse (most close to 0) – smooth signals and Fourier sinusoids – piecewise smooth signals and wavelets, … • Approximation – quantize/encode coeff sizes and locations • Transform coding examples: JPEG, MPEG, …
Background image of page 4
DSP Sensing • The typical sensing/compression setup – compress = transform, sort coefficients, encode – most computation at sensor lots of work to throw away >80% of the coefficients sample compress transmit receive decompress
Background image of page 5

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

View Full Document Right Arrow Icon
• Measure projections onto incoherent basis/frame • Reconstruct via optimization • Mild oversampling: • Highly asymmetrical (most computation at receiver ) [Donoho; Candes, Romberg, Tao] project transmit receive reconstruct Compressed Sensing (CS)
Background image of page 6
Compressed Sensing 101 • Foundation: Reconstruction from incoherent projections • Signal has sparse representation in some basis (ex: Fourier, wavelets, etc.) – WLOG assume signal is sparse in time domain • Take second, incoherent basis – elements of are not sparse in – random is incoherent with almost all • Measure signal via few linear projections
Background image of page 7

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

View Full Document Right Arrow Icon
Before CS - L2 • Goal: Given measurements find signal • Fewer rows than columns in measurement matrix Ill-posed : infinitely many solutions • Classical solution: least squares
Background image of page 8
• Goal: Given measurements find signal • Fewer rows than columns in measurement matrix
Background image of page 9

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

View Full Document Right Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 43

DCS_Asilomar_Nov2 - Distributed Compressed Sensing Dror...

This preview shows document pages 1 - 10. Sign up to view the full document.

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