## A Tensor Framework for Multidimensional Signal Processing (1994)

Venue: | Linkoping University, Sweden |

Citations: | 53 - 8 self |

### BibTeX

@TECHREPORT{Westin94atensor,

author = {Carl-fredrik Westin},

title = {A Tensor Framework for Multidimensional Signal Processing},

institution = {Linkoping University, Sweden},

year = {1994}

}

### Years of Citing Articles

### OpenURL

### Abstract

ii About the cover The figure on the cover shows a visualization of a symmetric tensor in three dimensions, G = λ1ê1ê T 1 + λ2ê2ê T 2 + λ3ê3ê T 3 The object in the figure is the sum of a spear, a plate and a sphere. The spear describes the principal direction of the tensor λ1ê1ê T 1, where the length is proportional to the largest eigenvalue, λ1. The plate describes the plane spanned by the eigenvectors corresponding to the two largest eigenvalues, λ2(ê1ê T 1 + ê2ê T 2). The sphere, with a radius proportional to the smallest eigenvalue, shows how isotropic the tensor is, λ3(ê1ê T 1 + ê2ê T 2 + ê3ê T 3). The visualization is done using AVS [WWW94]. I am very grateful to Johan Wiklund for implementing the tensor viewer module used. This thesis deals with filtering of multidimensional signals. A large part of the thesis is devoted to a novel filtering method termed “Normalized convolution”. The method performs local expansion of a signal in a chosen filter basis which