Compressed SensingCompressed SensingMobashir MohammadAditya KulkarniTobias Berte

Compressed SensingCompressed SensingMobashir MohammadAditya KulkarniTobias Berte www.phwiki.com

Compressed SensingCompressed SensingMobashir MohammadAditya KulkarniTobias Berte

Buckmaster, Bill, News Assignment Editor has reference to this Academic Journal, PHwiki organized this Journal Compressed SensingCompressed SensingMobashir MohammadAditya KulkarniTobias BertelsenMalay SinghHirak SarkarNir in addition to ika WanigasekaraYamilet Serrano LlerenaParvathy SudhirIntroductionMobashir Mohammad3

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The Data DelugeSensors: Better Stronger Faster Challenge:Exponentially increasing amounts of dataAudio, Image, Video, Weather, Global scale acquisition 45Sensing by SamplingSampleN6

Sensing by Sampling (2)SampleNCompressN >> LJPEG LLDecompressN >> LN7Compression: Toy Example8Discrete Cosine Trans as long as mationTrans as long as mation9

MotivationWhy go to so much ef as long as t to acquire all the data when most of the what we get will be thrown away Cant we just directly measure the part that wont end up being thrown away Donoho200410OutlineCompressed SensingConstructing Sparse Signal RecoveryConvex Optimization AlgorithmApplicationsSummary Future Work11Compressed SensingAditya Kulkarni12

What is compressed sensingA paradigm shift that allows as long as the saving of time in addition to space during the process of signal acquisition, while still allowing near perfect signal recovery when the signal is neededNyquist rate SamplingAnalog Audio SignalCompression (e.g. MP3)High-rateLow-rateCompressed Sensing13SparsityThe concept that most signals in our natural world are sparseOriginal imagec. Image reconstructed by discarding the zero coefficients14How It Works15

Dimensionality Reduction Problem16Sampling1718

19SparsityThe concept that most signals in our natural world are sparseOriginal imagec. Image reconstructed by discarding the zero coefficients2021

Constructing Tobias Bertelsen22RIP – Restricted Isometry PropertyThe distance between two points are approximately the same in the signal-space in addition to measure-space23RIP – Restricted Isometry PropertyImage: http://www.brainshark.com/brainshark/brainshark.net/portal/title.aspxpid=zCgzXgcEKz0z024

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R in addition to omized algorithm25Sub-Gaussian distribution26Johnson-Lidenstrauss Lemma27

Generalizing to RIP28R in addition to omized algorithm29Sparse in another base30

ReferencesEmmanuel C in addition to es, Compressive Sensing – A 25 Minute Tour, First EU-US Frontiers of Engineering Symposium, Cambridge, September 2010David Schneider, Camera Chip Makes Already-Compressed Images, IEEE Spectrum, Feb 2013T.Strohmer. Measure what should be measured: Progress in addition to Challenges in Compressive Sensing. IEEE Signal Processing Letters, vol.19(12): pp.887-893, 2012.Larry Hardesty, Toward practical compressed sensing, MIT news, Feb 2013Tao Hu in addition to Mitya Chklovvskii, Reconstruction of Sparse Circuits Using Multi-neuronal Excitation (RESCUME), Advances in Neural In as long as mation Processing Systems, 2009http://inviewcorp.com/technology/compressive-sensing/http://ge.geglobalresearch.com/blog/the-beauty-of-compressive-sensing/http://www.worldindustrialreporter.com/bell-labs-create-lensless-camera-through-compressive-sensing-technique/http://www.lablanche- in addition to -co.com/76THANK YOU77

Buckmaster, Bill News Assignment Editor

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