REKONSTRUKSI CITRA-WARNA DARI PENGINDERAAN KOMPRESIF DENGAN MATRIKS PENGUKURAN TEROPTIMASI

Transkripsi

1 REKONSTRUKSI CITRA-WARNA DARI PENGINDERAAN KOMPRESIF DENGAN MATRIKS PENGUKURAN TEROPTIMASI Endra Department of Computer Engineering Bina Nusantara University Agustus 2011

2 WHAT IS COMPRESSIVE SENSING? A Contemporary Paradox

3 WHAT IS COMPRESSIVE SENSING?

4 WHAT IS COMPRESSIVE SENSING? Candes, E.J., and Wakin, M.B., March. 2008, An Introduction to Compressive Sampling, IEEE Signal Processing Magazine., pp

5 WHAT IS COMPRESSIVE SENSING? When Sensing Meet Compression Automatically translates analog data into already compressed digital form.

6 Applications and Opportunities Of Compressive Sensing New Analog-to-Digital Converters (Analog to Information)

7 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.

8 COMPRESSIVE SENSING FRAMEWORK M 1 M N N K K 1 θ M 1 M K K 1 D θ S Sparse Measurement Matrix Sparse Coefficent Equivalent Dictionary Basis/Dictionary M N y x x If K N Complete (Basis) y D If K N Over-Complete (Dictionary)

9 PENELITIAN SEBELUMNYA 1. Emmanuel J. Candès and Terence Tao, 2006 Menggunakan random matriks untuk pengukuran/proyeksi kompresif dan - minimization untuk rekonstruksi 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 1 - minimization untuk rekonstruksi sinyal 1 dimensi dan memiliki eksak sparsity. p 4. Rick Chartrand and Wotao Yin, 2008 IRLS- - minimization untuk rekonstruksi sinyal 1 dimensi dan eksak sparsity, random matriks untuk pengukuran. 5. Endra, 2010 IRLS - p - minimization untuk rekonstruksi citra warna dari penginderaan kompresif, menggunakan random matriks untuk pengukuran. 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.

10 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 : T D : max d d Equivalent Dictionary, D, i j,1 i, j K i close to orthonormal Gram-Matrix of Equivalent Dictionary : G I min D G I 2 F min D D t D I 2 F

11 NUMERICAL EXPERIMENTS

12 RESULTS Citra Uji Lena Untuk algoritma Iteratively IRLS ell-pminimization peningkatkan PSNR mencapai 88 % Untuk algoritma OMP peningkatan PSNR mencapai 175 %

13 RESULTS Citra Uji Lena Random Matriks M = 19 % Optimasi Matriks Pengukuran IRLS-ell-p minimization OMP

14 RESULTS Citra Uji Baboon Untuk algoritma Iteratively IRLS ell-pminimization peningkatkan PSNR mencapai 68 % Untuk algoritma OMP peningkatan PSNR mencapai 108 %

15 RESULTS Citra Uji Baboon Random Matriks M = 16 % Optimasi Matriks Pengukuran IRLS-ell-p minimization OMP

16 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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