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Compressive Sensing applied on a Video Signal
KTH, School of Electrical Engineering (EES), Signal Processing.
2015 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Compressive Sensing has attracted a lot of attention over the last decade

within the areas of applied mathematics, computer science and electrical

engineering because of it suggesting that we can sample a signal under the

limit that traditional sampling theory provides. By then using dierent recovery

algorithms we are able to, theoretically, recover the complete original

signal even though we have taken very few samples to begin with. It has

been proven that these recovery algorithms work best on signals that are

highly compressible, meaning that the signals can have a sparse representation

where the majority of the signal elements are close to zero. In this

thesis we implement some of these recovery algorithms and investigate how

these perform practically on a real video signal consisting of 300 sequential

image frames. The video signal will be under sampled, using compressive

sensing, and then recovered using two types of strategies,

- One where no time correlation between successive frames is assumed, using

the classical greedy algorithm Orthogonal Matching Pursuit (OMP) and a

more robust, modied OMP called Predictive Orthogonal Matching Pursuit


- One newly developed algorithm, Dynamic Iterative Pursuit (DIP), which

assumes and utilizes time correlation between successive frames.

We then performance evaluate and compare these two strategies using the

Peak Signal to Noise Ratio (PSNR) as a metric. We also provide visual


Based on investigation of the data in the video signal, using a simple model

for the time correlation and transition probabilities between dierent signal

coecients in time, the DIP algorithm showed good recovery performance.

The main results showed that DIP performed better and better over time

and outperformed the PrOMP up to a maximum of 6 dB gain at half of the

original sampling rate but performed slightly below the PrOMP in a smaller

part of the video sequence where the correlation in time between successive

frames in the original video sequence suddenly became weaker.

Abstract [sv]

Compressive sensing har blivit mer och mer uppmarksammat under det

senaste decenniet inom forskningsomraden sasom tillampad matematik, datavetenskap

och elektroteknik. En stor anledning till detta ar att dess teori innebar

att det blir mojligt att sampla en signal under gransen som traditionell samplingsteori

innebar. Genom att sen anvanda olika aterskapningsalgoritmer

ar det anda teoretiskt mojligt att aterskapa den ursprungliga signalen. Det

har visats sig att dessaaterskapningsalgoritmer funkar bast pa signaler som

ar mycket kompressiva, vilket innebar att dessa signaler kan representeras

glest i nagon doman dar merparten av signalens koecienter ar nara 0 i

varde. I denna uppsats implementeras vissa av dessaaterskapningsalgoritmer

och vi undersoker sedan hur dessa presterar i praktiken pa en riktig videosignal

bestaende av 300 sekventiella bilder. Videosignalen kommer att undersamplas

med compressive sensing och sen aterskapas genom att anvanda 2

typer av strategier,

- En dar ingen tidskorrelation mellan successiva bilder i videosignalen antas

genom att anvanda klassiska algoritmer sasom Orthogonal Matching Pursuit

(OMP) och en mer robust, modierad OMP : Predictive Orthogonal

Matching Pursuit (PrOMP).

- En nyligen utvecklad algoritm, Dynamic Iterative Pursuit (DIP), som antar

och nyttjar en tidskorrelation mellan successiva bilder i videosignalen.

Vi utvarderar och jamfor prestandan i dessa tva olika typer av strategier

genom att anvanda Peak Signal to Noise Ratio (PSNR) som jamforelseparameter.

Vi ger ocksa visuella resultat fran videosekvensen.

Baserat pa undersokning av data i videosignalen visade det sig, genom att

anvanda enkla modeller, bade for tidskorrelationen och sannolikhetsfunktioner

for vilka koecienter som ar aktiva vid varje tidpunkt, att DIP algoritmen

visade battre prestanda an de tva andra tidsoberoende algoritmerna

under visa tidsekvenser. Framforallt de sekvenser dar videosignalen inneholl

starkare korrelation i tid. Som mest presterade DIP upp till 6 dB battre an

OMP och PrOMP .

Place, publisher, year, edition, pages
2015. , 62 p.
EES Examensarbete / Master Thesis, XR-EE-SB 2015:002
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
URN: urn:nbn:se:kth:diva-160909OAI: diva2:792223
Educational program
Master of Science in Engineering - Microelectronics; Master of Science - Wireless Systems
Available from: 2015-03-03 Created: 2015-03-03 Last updated: 2015-03-03Bibliographically approved

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