EndraDepartment of Computer Engineering

Bina Nusantara University15 – 16 Agustus 2011

REKONSTRUKSI CITRA-WARNA DARI PENGINDERAAN KOMPRESIF

DENGAN MATRIKS PENGUKURAN TEROPTIMASI

WHAT IS COMPRESSIVE SENSING ?

A Contemporary Paradox

WHAT IS COMPRESSIVE SENSING ?

WHAT IS COMPRESSIVE SENSING ?

Candes, E.J., and Wakin, M.B., March. 2008, An Introduction to Compressive Sampling, IEEE Signal Processing Magazine., pp. 21-30.

WHAT IS COMPRESSIVE SENSING ?

When Sensing Meet Compression

Automatically translates analog data into alreadycompressed digital form.

Applications and Opportunities Of Compressive Sensing

New Analog-to-Digital Converters (Analog to Information)

COMPRESSIVE SENSINGCOMPRESSIVE SENSING

1. The desired signals/images are sparse/compressible.

2. CS matrices satisfies RIP (Restricted IsometryProperty).

3. Reconstruction algorithms.

CS Theory Requires Three Aspects :

COMPRESSIVE SENSING FRAMEWORKCOMPRESSIVE SENSING FRAMEWORK

xy Dy

NM

x

Basis/Dictionary

Sparse Coefficent

Measurement Matrix

1M KN θ

1K

S

Sparse

D θ1M KM 1K

EquivalentDictionary

NM

If NK Complete

(Basis)

If Over-Complete

(Dictionary)

NK

1. Emmanuel J. Candès and Terence Tao, 2006 Menggunakan random matriks untuk pengukuran/proyeksi kompresif dan - minimization untuk rekonstruksi.

PENELITIAN SEBELUMNYAPENELITIAN SEBELUMNYA

1

2. J. A. Tropp and A. C. Gilbert, 2007 Menggunakan random matriks untuk pengukuran kompresif dan Orthogonal Matching Pursuit (OMP) untuk rekonstruksi.

3. M. Elad, 2007 Optimasi matriks pengukuran, OMP dan - minimization untuk rekonstruksi sinyal 1 dimensi dan memiliki eksak sparsity.

1

4. Rick Chartrand and Wotao Yin, 2008 IRLS- - minimization untuk rekonstruksi sinyal 1 dimensi dan eksak sparsity, random matriks untuk pengukuran.

p

5. Endra, 2010 IRLS - - minimization untuk rekonstruksi citra warna dari penginderaan kompresif, menggunakan random matriks untuk pengukuran.

p

Pada tulisan ini optimasi matriks pengukuran didasarkan pada metode Elad untuk pengukuran kompresif citra warna dan rekonstruksi menggunakan IRLS- - Minimization dan OMP sebagai perbandingan.

p

OPTIMIZED MEASUREMENT MATRIXOPTIMIZED MEASUREMENT MATRIX

Random Gaussian Matrix that fulfill the required property of CSmeasurement (Incoherency & RIP) usually to be used to encode thesignal.

can be optimized by reducing the mutual coherence :

ddD TiKjiji ,1,max: Equivalent Dictionary, D,

close to orthonormal

Gram-Matrix of Equivalent Dictionary :

IG 22 minminF

tDFD IDDIG

NUMERICAL EXPERIMENTS

RESULTS

Citra Uji Lena

Untuk algoritma Iteratively IRLS – ell-p-minimization peningkatkan PSNR mencapai 88 %

Untuk algoritma OMP peningkatan PSNR mencapai 175 %

RESULTS

Citra Uji Lena

M = 19 %

IRLS-ell-p minimization OMP

Random Matriks

Optimasi Matriks Pengukuran

RESULTS

Citra Uji Baboon

Untuk algoritma Iteratively IRLS – ell-p-minimization peningkatkan PSNR mencapai 68 %

Untuk algoritma OMP peningkatan PSNR mencapai 108 %

RESULTS

Citra Uji Baboon

M = 16 %

IRLS-ell-p minimization OMP

Random Matriks

Optimasi Matriks Pengukuran

Kesimpulan

Optimasi matriks pengukuran pada penginderaan kompresifcitra-warna dapat meningkatkan kualitas rekonstruksi citrauntuk kedua metode rekonstruksi yang digunakan yakniIteratively IRLS – ell-p - minimization dan OMP.

Untuk penelitian selanjutnya, peningkatan kinerja daripenginderaan kompresif dapat dilakukan denganmenggunakan kamus-basis lewat lengkap yang dipelajaridari sekumpulan besar citra dan optimasi matrikspengukuran dilakukan bersamaan dalam prosespembelajaran tersebut. Peningkatan lebih jauh lagi dilakukandengan memanfaatkan representasi block-sparse yangdipelajari dari sekumpulan besar citra untuk mengoptimasimatriks pengukuran.

REFERENCES[1] Michael Unser, Apr. 2000, Sampling—50 YearsAfter Shannon, Proceedings of the IEEE., vol.88, no. 4, pp. 569-587.

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REFERENCES

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[22] Endra, Oct. 2010, Color Image ReconstructionFrom Compressive Sensing Using IterativelyReweighted Least Squares- p –Minimization, inProc. Makassar International Conference onElectrical Engineering and Informatics, 2010.

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REFERENCES

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