Open AccessTensorial Model for Photolithography Aerial Image Simulation
Author(s) -
Caroline Fossati,
Salah Bourennane,
Romuald Sabatier,
Antonio Di Giacomo
Publication year - 2009
Publication title -
advances in optoelectronics
Language(s) - English
Resource type - Journals
eISSN - 1687-5648
pISSN - 1687-563X
DOI - 10.1155/2009/457549
Subject(s) - multilinear algebra , singular value decomposition , tensor (intrinsic definition) , tensor algebra , multilinear map , aerial image , rank (graph theory) , algorithm , eigenvalues and eigenvectors , square (algebra) , computer science , image (mathematics) , mathematics , artificial intelligence , algebra over a field , pure mathematics , geometry , combinatorics , physics , current algebra , quantum mechanics , division algebra , jordan algebra , filtered algebra
In this paper, we propose to adapt the multilinear algebra tools to the tensor of Transmission Cross-Coefficients (TCC) values for aerial image simulation in order to keep the datatensor as a whole entity. This new approach implicitly extends the singular value decomposition (SVD) to tensors, that is, Higher Order SVD or TUCKER3 tensordecomposition which is used to obtain lower rank-(1,2,3,4) tensor approximation (LRTA (1,2,3,4)). This modelrequires an Alternating Least Square (ALS) process known as TUCKALS3 algorithm. The needed number of kernels is estimatedusing two adapted criteria, well known in signal processing and information theory. For runtime improvement, we use the fixedpoint algorithm to calculate only the needed eigenvectors. This new approach leads to a fast and accurate algorithm to computeaerial images
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