Aplikasi Dekomposisi Nilai Singlar Matriks Quaternion terhadap Perbaikan Citra Low dan High Pass Filtering

Regita Agustin Wahyu Fibriyanti, Karyati Karyati

Abstract


Dekomposisi nilai singular matriks quaternion (Quaternion Singular Value Decomposition/SVDQ) sangat berguna dalam pengolahan citra, seperti dalam kompresi ukuran gambar, eigen-images, dan perbaikan kualitas citra, khususnya perbaikan suatu citra low pass filtering dan high pass filtering. Tujuan penelitian ini adalah mengetahui bagaimana aplikasi dekomposisi nilai singular matriks quaternion pada perbaikan suatu citra low pass filtering dan high pass filtering, serta memberikan suatu aplikasi berbasis GUI MATLAB. Dasar dari dekomposisi nilai singular matriks quaternion didapatkan dengan menggunakan representasi terhadap matriks kompleks, dengan kata lain menggunakan isomorfisma matriks quaternion terhadap matriks kompleks. Hal itu bertujuan untuk mempermudah pendekomposisian matriks quaternion. Matriks quaternion tidak lepas dari nilai eigen matriks quaternion. Selanjutnya, nilai eigen matriks qauternion dapat dihitung menggunakan nilai eigen dari matriks kompleksnya. Melalui dekomposisi nilai singular matriks quaternion, diperoleh perbaikan citra low pass filtering dan high pass filtering yang hampir menyerupai citra aslinya. Untuk  perbaikan citra low pass filtering berhenti pada  dan untuk high pass filtering berhenti pada α=0,97.


Keywords


dekomposisi nilai singular; quaternion; matriks kompleks; low pass filtering; high pass filtering

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References


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DOI: https://doi.org/10.21831/jsd.v11i1.41951

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