On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
Separierbarkeit zweidimensionaler Filter
Mustererkennung 1990, 12. DAGM-Symposium,
Recursive Gaussian Derivative Filters
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 1 - Volume 1
Multidimensional filtering based on a tensor approach
Signal Processing
Improving Deriche-style Recursive Gaussian Filters
Journal of Mathematical Imaging and Vision
Multivariate Regression and Machine Learning with Sums of Separable Functions
SIAM Journal on Scientific Computing
Tensor Decompositions and Applications
SIAM Review
Journal of Computational and Applied Mathematics
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Utilizing separation to decompose a local filter mask is a well-known technique to accelerate its convolution with discrete two-dimensional signals such as images. However, many modern days' applications involve higher-dimensional, discrete data that needs to be processed but whose inherent spatial complexity would render immediate/naive convolutions computationally infeasible. In this paper, we show how separability of general higher-order tensors can be leveraged to reduce the computational effort for discrete convolutions from super-polynomial to polynomial (in both the filter mask's tensor order and spatial expansion). Thus, where applicable, our method compares favorably to current tensor convolution methods and, it renders linear filtering applicable to signal domains whose spatial complexity would otherwise have been prohibitively high. In addition to our theoretical guarantees, we experimentally illustrate our approach to be highly beneficial not only in theory but also in practice.