20080701-CS - COMPRESSED SENSING Luis Mancera Visual...

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    COMPRESSED SENSING Luis Mancera Visual Information Processing Group Dep. Computer Science and AI Universidad de Granada
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    CONTENTS 1. WHAT? Introduction to Compressed Sensing (CS) 2. HOW? Theory behind CS 3. FOR WHAT PURPOSE? CS applications 4. AND THEN? Active research and future lines
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    CONTENTS 1. WHAT? Introduction to Compressed Sensing (CS) 2. HOW? Theory behind CS 3. FOR WHAT PURPOSE? CS applications 4. AND THEN? Active research and future lines
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    Transmission scheme Sample Receive Compress Decompress N K N >> K Transmit K N Why so many samples? Natural signals (sparse/compressible) no significant perceptual loss Brick wall to performance
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    Shannon/Nyquist theorem Shannon/Nyquist theorem tell us to use a sampling rate of 1/(2W) seconds, if W is the highest frequency of the signal This is a worst-case bound for ANY band- limited signal Sparse / compressible signals is a favorable case CS solution: melt sampling and compression
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    Compressed Sensing (CS) Compressed Sensing Receive Reconstruct M K < M << N Transmit M N Recover sparse signals by directly acquiring compressed data Replace samples by measurements What do we need for CS to success?
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    We now how to Sense  Compressively I’m glad this battle is over. Finally my military period is over. I will now come back to Motril and get married, and then I will grow up pigs as I have always wanted to do Aye Cool! Do you mean you’re glad this battle is over because now you’ve finished here and you will go back to Motril, get married, and grow up pigs as you always wanted to?
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    What does CS need? Nice sensing dictionary Appropriate sensing A priori knowledge Recovery process Wie lange wird das nehmen? What? Saint Roque’s dog has no tail I know this guy so much that I know what he means Cool! Words Idea
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    CS needs: Nice sensing dictionary Appropriate sensing A priori knowledge Recovery process SPARSENESS RANDOMNESS INCOHERENCE OPTIMIZATION
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    Sparseness: less is more A stranger approaching a hut by the only known road: the valley Dictionary : How to express it? Idea: “He was advancing by the only road that was ever traveled by the stranger as he approached the Hut; or, he came up the valley” Wyandotte Combining elements… J.F. Cooper E.A . Poe Combining elements… Hummm, you could say the same using less words… “He was advancing by the valley, the only road traveled by a stranger approaching the Hut” Comments to Wyandotte SPARSER
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    Sparseness: less is more Sparseness : Property of being small in numbers or amount, often scattered over a large area [Cambridge Advanced Learner’s Dictionary] A CERTAIN DISTRIBUTION A SPARSER DISTRIBUTION
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  Sparseness: less is more Original Einstein Taking 10% pixels
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This note was uploaded on 05/28/2010 for the course EE EE564 taught by Professor Runyiyu during the Spring '10 term at Eastern Mediterranean University.

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20080701-CS - COMPRESSED SENSING Luis Mancera Visual...

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