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
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 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
NK
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
KN
Complete (Basis)
If
KN
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.
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