Compressed Sensing Project Hassan 2010315440

8/6/2019 Compressed Sensing Project Hassan 2010315440

1/16

1

Image Compression via

Compressive Sampling

Digital Image Processing

Hassan (Student id =2010315440)

Department of Computer Engineering

Final Project


2/16

2

Sequence of presentation

qIntroduction and Motivation

qProblem Statement

qMethodology

qImplementation

qResults

qConclusion


3/16

3

Introduction

The Shannon/Nyquist sampling theorem says we must samplea single at least two times faster than its bandwidth

However we may end up with too many samples and mustcompress in order to store or transmit them

In Past , Transform coding is used to sample-then-compress animage

But it suffers from three inefficiencies:

start with large number of samples N

encoder must compute all of the N transform coefficients

the overhead of encoding the locations of the large coefficients.


4/16

4

Motivation

Image compression algorithm convert high-resolution image to small bit streamBut is there a way to avoid the large date setto begin with ?

The existing image compression methods(e.g. Jpeg2000, SPIHT) are vulnerable to bitlossWe require a compressions scheme thattackles these loses


5/16

5

CS Theory

Compressive sensing (CS), also known ascompressive sampling, is a new sensing and samplingparadigm, which involves three major aspect:

Sparse representation

CS measurements taking

CS reconstruction


6/16

6

Practical examples (1/2)

qOne of the first prototype demonstrations of compressed sensing is the singlepixel camera, developed by Rice University

q

q

q

q

q

q

q

q

Test image (16384 pixels) and CS reconstruction using 1600 and 3300 measurements(http://dsp.rice.edu/cscamera)

q


7/16

7

Practical examples (2/2)

q

q

q

q

q

q

q

q

q

q

MRI image of a mouse heart, and CS reconstruction using 20% of availablemeasurements


8/16

8

Problem statement (1/2)


9/16

9

Problem statement (2/2)


10/16

10

Methodology

Choose measurement matrix as IID GaussianRandom matrix

The reconstruction algorithm is a LinearAlgebra Problem!!

Minimum l1 norm reconstruction:

This is a convex optimization problem that can be solvedusing Linear Programing


11/16

11

Implementation in MTES(1/2)


12/16

12

MTES Implementation (2/2)

Encoder

Decoder


13/16

13

Results (1/2)

a) Original cameraman Image b) Reconstructed cameraman Image

c) Original Lena Image b) Reconstructed Lena Image

From Matlab


14/16

14

Results (2/2)

e) Original 32x32 section ofMRIscan Image

f)Reconstructed 32x32 section of MRIscanImage

g) Original 128x128 hardware Image h) reconst. 128x128 hardware ImageFrom Matlab


15/16

15

Conclusions

Compressed sensing is a fairly new paradigm,but is already being used in practical settings,for instance to speed up MRI scans by requiringfewer measurements to achieve a given amount

of resolution.

It is better to divide the image into blocks ratherthen taking a whole image.


16/16

16

References

B. Han et all., Image representation by compressed sensing, inIEEE Int. Conf. Image Process.(ICIP08),Chenwei Deng et all , Robust Image Compression Based onCompressive Sensing, ICME 2010

Y.F. Zhang, S.L. Mei, and Q.Q. Chen, A novel image videocoding method based on compressed sensing theory, in IEEE Int.conf. Acoustics, Speech. Signal Process. (ICASSP08)Richard Baraniuk, A Lecture on Compressive Sensing, IEEESignal Processing Magazine, July 2007

E.J. Cand`es, M.B. Wakin, and S.P. Boyd, Enhancing sparsity byreweighted 1 minimization, J. Fourier Analy. and Applic., vol. 14,no. 5, pp. 877905, Oct. 2008.

Documents

Compressed Sensing Project Hassan 2010315440