On the computational benefit of tensor separation for high-dimensional discrete convolutions

DOI10.1007/s11045-010-0131-2zbMath1256.93028OpenAlexW1965562399MaRDI QIDQ1937804

Michael Mai, Jan-P. Calliess, Sebastian Pfeiffer

Publication date: 1 February 2013

Published in: Multidimensional Systems and Signal Processing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11045-010-0131-2

zbMATH Keywords

imagetensordecompositionconvolutionseparabilityspatial expansiondiscrete two-dimensional signalslocal filter maskmulti-dimensiona element (muxel)multi-dimensional filtering

Mathematics Subject Classification ID

System structure simplification (93B11) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Large-scale systems (93A15)

Uses Software

• ITK

Cites Work

• Tensor Decompositions and Applications
• Fast and accurate tensor approximation of a multivariate convolution with linear scaling in dimension
• Multidimensional filtering based on a tensor approach
• Dimensionality reduction in higher-order signal processing and rank-\((R_1,R_2,\ldots,R_N)\) reduction in multilinear algebra
• Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
• Rank-One Approximation to High Order Tensors
• Multivariate Regression and Machine Learning with Sums of Separable Functions
• Computer-aided design of separable two-dimensional digital filters
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
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