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EndraDepartment of Computer Engineering
Bina Nusantara University15 – 16 Agustus 2011
REKONSTRUKSI CITRA-WARNA DARI PENGINDERAAN KOMPRESIF
DENGAN MATRIKS PENGUKURAN TEROPTIMASI
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
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.
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