REKONSTRUKSI CITRA-WARNA DARI PENGINDERAAN

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REKONSTRUKSI CITRA-WARNA
DARI PENGINDERAAN KOMPRESIF
DENGAN MATRIKS PENGUKURAN TEROPTIMASI
Endra
Department of Computer Engineering
Bina Nusantara University
15 – 16 Agustus 2011
WHAT IS COMPRESSIVE SENSING ?
A Contemporary Paradox
Candes, E.J., and Wakin, M.B., March. 2008,
An Introduction to Compressive Sampling,
IEEE Signal Processing Magazine., pp. 21-30.
When Sensing Meet Compression
Automatically translates analog data into already
compressed digital form.
Applications and Opportunities
Of Compressive Sensing
New Analog-to-Digital
Converters (Analog to
Information)
COMPRESSIVE SENSING
CS Theory Requires Three Aspects :
1. The desired signals/images are sparse/compressible.
2. CS matrices satisfies RIP (Restricted IsometryProperty).
3. Reconstruction algorithms.
COMPRESSIVE SENSING FRAMEWORK
M 1
M N
NK
K 1
θ
K 1
θ
M K
D
M 1
S
Sparse
Measurement Matrix
Sparse
Coefficent
Basis/Dictionary
y  x
x  
y    D
Equivalent
Dictionary
M  N
If
KN

Complete
(Basis)
If
KN

Over-Complete
(Dictionary)
PENELITIAN SEBELUMNYA
1. Emmanuel J. Candès and Terence Tao, 2006 
pengukuran/proyeksi kompresif dan  1
Menggunakan random matriks untuk
- minimization untuk rekonstruksi.
 Menggunakan random matriks untuk pengukuran
kompresif dan Orthogonal Matching Pursuit (OMP) untuk rekonstruksi.
2. J. A. Tropp and A. C. Gilbert, 2007
 Optimasi matriks pengukuran, OMP dan  1 - minimization untuk
rekonstruksi sinyal 1 dimensi dan memiliki eksak sparsity.
3. M. Elad, 2007
IRLS-  p - minimization untuk rekonstruksi sinyal
1 dimensi dan eksak sparsity, random matriks untuk pengukuran.
4. Rick Chartrand and Wotao Yin, 2008 
IRLS -  p - minimization untuk rekonstruksi citra warna dari
penginderaan kompresif, menggunakan random matriks untuk pengukuran.
5. Endra, 2010 
Pada tulisan ini optimasi matriks pengukuran didasarkan pada
metode Elad untuk pengukuran kompresif citra warna dan
rekonstruksi menggunakan IRLS-  p - Minimization dan OMP
sebagai perbandingan.
OPTIMIZED MEASUREMENT MATRIX
Random Gaussian Matrix that fulfill the required property of CS
measurement (Incoherency & RIP) usually to be used to encode the
signal.
can be optimized by reducing the mutual coherence :
 D  : max
i  j ,1 i , j  K
d d 
T
i
Equivalent Dictionary, D,
close to orthonormal
Gram-Matrix of Equivalent Dictionary :
G  I
min
D
G  I
2
F
 min
D
t
2
D D  I
F
NUMERICAL EXPERIMENTS
RESULTS
Citra Uji Lena
Untuk algoritma
Iteratively IRLS – ell-pminimization
peningkatkan PSNR
mencapai 88 %
Untuk algoritma OMP
peningkatan PSNR
mencapai 175 %
RESULTS
Citra Uji Lena
Random
Matriks
M = 19 %
Optimasi
Matriks
Pengukuran
IRLS-ell-p minimization
OMP
RESULTS
Citra Uji Baboon
Untuk algoritma
Iteratively IRLS – ell-pminimization
peningkatkan PSNR
mencapai 68 %
Untuk algoritma OMP
peningkatan PSNR
mencapai 108 %
RESULTS
Citra Uji Baboon
Random
Matriks
M = 16 %
Optimasi
Matriks
Pengukuran
IRLS-ell-p minimization
OMP
Kesimpulan
Optimasi matriks pengukuran pada penginderaan kompresif
citra-warna dapat meningkatkan kualitas rekonstruksi citra
untuk kedua metode rekonstruksi yang digunakan yakni
Iteratively IRLS – ell-p - minimization dan OMP.
Untuk penelitian selanjutnya, peningkatan kinerja dari
penginderaan
kompresif
dapat
dilakukan
dengan
menggunakan kamus-basis lewat lengkap yang dipelajari
dari sekumpulan besar citra dan optimasi matriks
pengukuran
dilakukan
bersamaan
dalam
proses
pembelajaran tersebut. Peningkatan lebih jauh lagi dilakukan
dengan memanfaatkan representasi block-sparse yang
dipelajari dari sekumpulan besar citra untuk mengoptimasi
matriks pengukuran.
REFERENCES
[1] Michael Unser, Apr. 2000, Sampling—50 Years
After Shannon, Proceedings of the IEEE., vol.
88, no. 4, pp. 569-587.
[2] David L. Donoho, Apr. 2006, Compressed
Sensing, IEEE Transactions on Information
Theory., vol. 52, no. 4, pp. 1289-1306.
[3] Emmanuel J. Candès, Justin Romberg, and
Terence Tao, Feb. 2006, Robust Uncertainty
Principles: Exact Signal Reconstruction From
Highly Incomplete Frequency Information,
IEEE Transactions on Information Theory., vol.
52, no. 2, pp. 489-509.
[4] E. Candès, J. Romberg, and T. Tao, Aug. 2006 ,
Stable signal recovery from incomplete and
inaccurate measurements, Comm. Pure Appl.
Math., vol. 59, no. 8, pp. 1207–1223.
[5] Emmanuel J. Candès and Terence Tao, Dec.
2006, Near-Optimal Signal Recovery From Random
Projections: Universal Encoding Strategies?, IEEE
Transactions on Information Theory., vol. 52, no. 12,
pp. 5406-5425.
[6] Candes, E.J., and Wakin, M.B., March. 2008,
An Introduction to Compressive Sampling,
[7] Jing Wu and Ye Li, Nov. 2009, Low-complexity
Video Compression for Capsule Endoscope
Based on Compressed Sensing Theory, in Proc.
International Conference of the IEEE
Engineering in Medicine and Biology Society,
EMBC 2009., pp. 3727-3730.
[8] Lustig, M., Donoho, D.L., Santos, J.M., Pauly,
J.M., March. 2008, Compressed Sensing MRI,
[9] Haupt, J., Bajwa, W.U., Rabbat, M., and
Nowak, R., March. 2008, Compressed Sensing
for Networked Data, IEEE Signal Processing
Magazine., pp. 92-101.
[10] Peng Zhang, Chen Chen, and Minrun Liu,
Nov. 2009, The Application of Compressed
Sensing in Wireless Sensor Network, in Proc.
International Conference on Wireless
Communication & Signal Processing, WCSP
2009., pp. 1-5.
REFERENCES
[11] Lei Yu, Yi Yang, Hong Sun, and Chu He, Oct.
2009, Turbo-like Iterative Thresholding for SAR
Image Recovery from Compressed Measurements,
in Proc.2nd Asian Pacific Conference on Synthetic
Aperture Radar, APSAR 2009., pp. 664-667.
[16] Duarte, M.F., Davenport, M.A., Takhar, D.,
Laska, J.N., Ting Sun, Kelly, K.F., and
Baraniuk, R.G., March. 2008, Single-Pixel
Imaging via Compressive Sampling, IEEE
Signal Processing Magazine., pp. 83-91.
[12] Matthew A. Herman and Thomas Strohmer,
Jun. 2009, High-Resolution Radar via Compressed
Sensing, IEEE Transactions on Signal Processing.,
pp. 2275-2284.
[17] Jianwei Ma, Oct. 2009, A Single-Pixel Imaging
System for Remote Sensing by Two-Step
Iterative Curvelet Thresholding, IEEE
Geoscience and Remote Sensing Letters., vol. 6,
no. 4, pp. 676-680.
[13] A Anil Kumar and Anamitra Makur, Jan. 2009,
Lossy Compression of Encrypted Image by
Compressive Sensing Technique, in Proc. IEEE
Region 10 Conference TENCON 2009., pp. 1-5.
[18] Jianwei Ma, Apr. 2009, Single-Pixel Remote
Sensing, IEEE Geoscience and Remote Sensing
Letters., vol. 6, no. 2, pp. 199-203.
[14] Adem Orsdemir, H. Oktay Altun, Gaurav
Sharma, and Mark F. Bocko, Nov. 2008, On
The Security and Robustness of Encryption Via
Compressed Sensing, in Proc. IEEE Military
Communications Conference, MILCOM 2008.,
pp. 1-7.
[15] Justin Romberg, March. 2008, Imaging via
Compressive Sensing, IEEE Signal Processing
Magazine., pp. 14-20.
[19] Mark A. Davenport, Petros T. Boufounos,
Michael B. Wakin, and Richard G. Baraniuk,
Apr. 2010, Signal Processing With Compressive
Measurements, IEEE Journal of Selected Topics
in Signal Processing., vol. 4, no. 2, pp. 445-460.
[20] D.S. Taubman and M.W. Marcellin, 2001,
JPEG 2000: Image Compression
Fundamentals, Standards and Practice,
Norwell, MA: Kluwer.
REFERENCES
[21] E. Candès and J. Romberg, 2007, Sparsity and
incoherence in compressive sampling, Inverse
Prob., vol. 23, no. 3, pp. 969–985.
[22] Endra, Oct. 2010, Color Image Reconstruction
From Compressive Sensing Using Iteratively
Reweighted Least Squares- p –Minimization, in
Proc. Makassar International Conference on
Electrical Engineering and Informatics, 2010.
[23] M. Elad, Dec. 2007, Optimized projections for
compressed sensing,” IEEE Transactions on
Signal Processing, vol. 55, no. 12, pp. 5695–
5702.
[24] Rick Chartrand and Wotao Yin, Apr. 2008,
Iteratively Reweighted Algorithms for
Compressive Sensing, in Proc. IEEE
International Conference on Acoustics, Speech
and Signal Processing, ICASSP 2008., pp.
3869-3872.
[25] J. A. Tropp and A. C. Gilbert, 2007, Signal
recovery from random measurements via
orthogonal matching pursuit,” IEEE
Transactions on Information Theory, vol. 53,
no. 12, pp. 4655–4666.
[26] David L. Donoho and Xiaoming Huo, Nov.
2001, Uncertainty Principles and Ideal Atomic
Decomposition, IEEE Transactions on
Information Theory., vol. 47, no. 7, pp. 28452862.
[27] K. Rosenblum, L. Zelnik-Manor, and Y. C.
Eldar, “Dictionary optimization for block sparse
representations,” arXiv.org 1005.0202.
submitted to IEEE Trans. Signal Process., May
2010.
[28] Kevin Rosenblum, Lihi Zelnik-Manor, Yonina
C. Eldar, Sept. 2010, Sensing Matrix
Optimization for Block-Sparse Decoding, preprint[
Online]. Available:
http://arxiv.org/PS_cache/arxiv/pdf/1009/1009.1
533v1.pdf
REFERENCES
[29] Petros Boufounos, Justin Romberg and Richard
Baraniuk, “Compressive Sensing : Theory
and Applications,” IEEE Int. Conf. on Acoustics,
Speech and Signal Processing (ICASSP), Las
Vegas, Nevada, Apr. 2008 [Online]. Available:
http://www.ece.rice.edu/~richb/talks/cs-tutorialICASSP-mar08.pdf.
[30] Jianwei Ma., “Data Recovery from Compressed
Measurement”, School of Aerospace, Tsinghua
University, Beijing.
[31] E. Candès, Electrical Engineering Colloquium,
University of Washington, December 2010.
[32] Michael Elad, Optimized Projection Directions
for Compressed Sensing, The IV Workshop on
SIP & IT Holon Institute of Technology June
20th, 2007.
[33] Michael Elad, Sparse & Redundant
Representation Modeling of Images, Summer
School on Sparsity in Image and Signal
Analysis, Holar, Iceland, August 15 – 20 , 2010.

REKONSTRUKSI CITRA-WARNA DARI PENGINDERAAN

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