Judul: Deteksi Tumpahan Minyak Dan Perubahan Konsentrasi Klorofil-A Dari Citra Modis Di Perairan Celah Timor
Abstrak: Minyak yang berasal dari kebocoran ladang minyak lepas pantai Montara telah mencemari laut Australia hingga Laut Indonesia. Proyek minyak lepas pantai tersebut gagal dalam melakukan pengeboran pada 21 Agustus 2009 lalu. Pencemaran minyak diduga dapat mengurangi aktifitas fotosintesis oleh fitoplankton karena lapisan tipis minyak dipermukaan dapat mengurangi penetrasi cahaya matahari dan mengurangi difusi oksigen. Kelimpahan fitoplankton dapat diduga melalui parameter klorofil yaitu pigmen fotosintesis yang dimiliki oleh fitoplankton. Penelitian ini bertujuan untuk mengamati nilai reflektansi spektral pada perairan yang terkena tumpahan minyak dan membandingkan nilai klorofil pada daerah tumpahan minyak dan daerah yang tidak terkena tumpahan minyak. Penelitian ini mengambil lokasi pada wilayah tumpahan minyak Laut Australia hingga Laut Timor pada koordinat 90 LS-150 LS dan 1210 BT-1280 BT. Pengolahan data dilakukan di Laboratorium Penginderaan Jauh dan Sistem Informasi Geografis, Ilmu dan Teknologi Kelautan, FPIK – IPB pada bulan Maret – Juni 2011. Data yang digunakan ialah citra MODIS Level 1b resolusi 250 m, 500 m dan 1 km pada tanggal 30 Agustus 2009 dan 24 September 2009; citra MODIS level 3 composite mingguan selama periode 5 tahun (2005-2006) dan composite bulanan (2008-2009); serta data angin. Perangkat lunak yang digunakan untuk mengolah citra meliputi Idrisi Andes, HEG WIN dan SeaDAS. Berdasarkan citra MODIS RGB band 13, 12 dan 9 terlihat bahwa tumpahan minyak berwarna lebih gelap dari perairan sekitarnya. Hasil dari nilai spektral pada panjang gelombang visible (merah, biru dan hijau) terlihat lebih rendah pada perairan yang tertutup minyak dibandingkan dengan perairan tanpa minyak. Hal ini disebabkan karena daerah minyak yang lebih gelap akan memantulkan energi yang lebih rendah sehingga nilai spektral juga akan lebih rendah. Konsentrasi klorofil harian juga menunjukkan hal yang sama yakni terjadi penurunan pada wilayah tumpahan minyak. Minyak yang menutupi permukaan akan menghalangi cahaya masuk perairan sehingga akan menghambat klorofil untuk berfotosintesis Hal ini, menyebabkan klorofil terlihat rendah dari sensor MODIS. Konsentrasi klorofil spasial dengan rata-rata bulanan menunjukkan kisaran nilai yang lebih rendah pada bulan terjadinya tumpahan minyak yaitu September- November 2009. Konsentrasi klorofil temporal rata-rata mingguan selama periode waktu 5 tahun (2006-2010) menunjukkan adanya pola fluktuasi menurun pada saat terjadi tumpahan minyak.
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Judul: Deteksi Tumpahan Minyak Montara di Laut Timor Menggunakan Citra MODIS dengan Berbagai Algoritma
Abstrak: Oil Spill in the Timor Sea that occurring in 2009 has caused oil expansion to an area of 10.842.81 km2. The Oil spill was successfully detected by MODIS imagery. The purpose of this study was to compare the detection of oil results from various algorithms with MODIS imagery and it’s visual appearances. The algorithm used is Oil Spill Index, Flourecence Index, Sea Surface Temperature (SST) Callison, Principal Component Analysis (PCA), and Normalized Difference Vegetation Index (NDVI). The appearance of oil spill in MODIS image extracted using oil spill index and flourecence index was brighter than the surrounding water bodies and has higher pixel values, while the appearance of oil spill on PCA and NDVI algorithms appeared darker than the surrounding water bodies and has a lower pixel value. The test accuracy of the algorithms are, 41%, 46%, 41%, and 60%, respectively.
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Judul: The Construction of Greedy SVP LLL Algorithm
Abstrak: A lattice is a set of all integer linear combination of a set of linearly independent vectors in ℝ𝑛���. The independent vectors are called bases of lattice. Any lattice can be generated from many bases, and these bases have the same cardinality. In the lattice, the most fundamental and renowned problem is the Shortest Vector Problem (SVP). SVP is a tracking problem of the shortest nonzero vector in a lattice with equivalent bases. In two dimensions, SVP problem has resolved exactly by Gauss’ algorithm. When the lattice dimension is higher than two, A.K. Lenstra, H.W. Lenstra and L. Lovasz gave a LLL algorithm to compute approximation of nonzero shortest vector in the lattice. Reduced bases solution obtained from LLL algorithm still be an approximation and has polynomial running time of arbitrary dimension which large enough. In 1994, Schnoor and Euchner modified this LLL algorithm as a new variant which later was named deep insertion LLL algorithm. This algorithm is a modified version of the LLL algorithm to the terms of the exchange step to improve the accuracy of output of LLL reduced bases and applying it to the subset sum problem. The purpose of this research are: (1) Reconstruct the LLL algorithm and deep insertion LLL algorithm using a geometric approach. (2) Construct a greedy SVP LLL algorithm. (3) Implement the three algorithms in a symbolic programming language, and evaluate them experimentally. A bases ℬ=[𝐛���1,𝐛���2,…,𝐛���𝑛���] in ℝ𝑚��� is called reduced LLL with parameter 𝛿��� if satisfies: (a) |𝜇���𝑗���𝑖���|≤12, for every integer 𝑖���,𝑗��� with 1≤𝑖���<𝑗���<𝑛���. (b)𝛿���‖𝜋���𝑗���(𝐛���𝑗���)‖2≤‖𝜋���𝑗���(𝐛���𝑗���+1)‖2, for 𝑗���=1,2,…,𝑛���−1,where 𝛿��� is a reduced parameter of real numbers with 14<𝛿���<1. The first requirement is the reduced basis 𝛿��� must “nearly orthogonal” and in its computation case, this requirement can be reached out by using the Gram-Schmidt’s orthogonalization. While the second requirement is called exchange step, or used to called as Lovasz condition. By using both of these requirements, then they establish the LLL algorithm. Then, Schnoor and Euchner modify the LLL algorithm based on the requirements of the exchange step called the deep insertion LLL algorithm, where the exchange step is based on the comparison of the projected vector in orthogonal complement [𝐛���1,𝐛���2,…,𝐛���𝑘���−1]⊥ after j-th reduction. To construct greedy SVP LLL algorithm, the requirements of the exchange step is based on purely by comparing norm of lattice 𝐛���𝑗��� with norm lattice 𝐛���𝑖��� for 𝑖���=1,2,3…,𝑗���−1. The process of insertion reduced vector after the exchange step also has done greedily. Then, we calculate the number of arithmetic operation in greedy SVP LLL algorithm for further analysis. The result of our exprimentation for three algorithms on the certain matrix size shows that the running time of the three algorithms increases propotional to the size of the matrix. The result also shows that by using 𝛿���=34 for the LLL algorithm and the deep insertion LLL algorithm, and the greedy SVP LLL algorithm which is a new variant made by using no parameter of 𝛿���, outperform of the other of two previous algorithm in terms of speed with the same output.
Keyword: LLL algorithm, LLL deep insertion algorithm, greedy SVP LLL algorithm