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Advanced tensor based signal processing techniques for wireless communication systems and biomedical signal processing
Many observed signals in signal processing applications including wireless communications, biomedical signal processing, image processing, and machine learning are multi-dimensional. Tensors preserve the multi-dimensional structure and provide a natural representation of these signals/data. Moreover, tensors provide often an improved identifiability. Therefore, we benefit from using tensor algebra in the above mentioned applications and many more. In this thesis, we present the benefits of utilizing tensor algebra in two signal processing areas. These include signal processing for MIMO (Multiple-Input Multiple-Output) wireless communication systems and biomedical signal processing. Moreover, we contribute to the theoretical aspects of tensor algebra by deriving new properties and ways of computing tensor decompositions. Often, we only have an element-wise or a slice-wise description of the signal model. This representation of the signal model does not reveal the explicit tensor structure. Therefore, the derivation of all tensor unfoldings is not always obvious. Consequently, exploiting the multi-dimensional structure of these models is not always straightforward. We propose an alternative representation of the element-wise multiplication or the slice-wise multiplication based on the generalized tensor contraction operator. Later in this thesis, we exploit this novel representation and the properties of the contraction operator such that we derive the final tensor models. There exist a number of different tensor decompositions that describe different signal models such as the HOSVD (Higher Order Singular Value Decomposition), the CP/PARAFAC (Canonical Polyadic / PARallel FACtors) decomposition, the BTD (Block Term Decomposition), the PARATUCK2 (PARAfac and TUCker2) decomposition, and the PARAFAC2 (PARAllel FACtors2) decomposition. Among these decompositions, the CP decomposition is most widely spread and used. Therefore, the development of algorithms for the efficient computation of the CP decomposition is ...
Advanced tensor based signal processing techniques for wireless communication systems and biomedical signal processing
Many observed signals in signal processing applications including wireless communications, biomedical signal processing, image processing, and machine learning are multi-dimensional. Tensors preserve the multi-dimensional structure and provide a natural representation of these signals/data. Moreover, tensors provide often an improved identifiability. Therefore, we benefit from using tensor algebra in the above mentioned applications and many more. In this thesis, we present the benefits of utilizing tensor algebra in two signal processing areas. These include signal processing for MIMO (Multiple-Input Multiple-Output) wireless communication systems and biomedical signal processing. Moreover, we contribute to the theoretical aspects of tensor algebra by deriving new properties and ways of computing tensor decompositions. Often, we only have an element-wise or a slice-wise description of the signal model. This representation of the signal model does not reveal the explicit tensor structure. Therefore, the derivation of all tensor unfoldings is not always obvious. Consequently, exploiting the multi-dimensional structure of these models is not always straightforward. We propose an alternative representation of the element-wise multiplication or the slice-wise multiplication based on the generalized tensor contraction operator. Later in this thesis, we exploit this novel representation and the properties of the contraction operator such that we derive the final tensor models. There exist a number of different tensor decompositions that describe different signal models such as the HOSVD (Higher Order Singular Value Decomposition), the CP/PARAFAC (Canonical Polyadic / PARallel FACtors) decomposition, the BTD (Block Term Decomposition), the PARATUCK2 (PARAfac and TUCker2) decomposition, and the PARAFAC2 (PARAllel FACtors2) decomposition. Among these decompositions, the CP decomposition is most widely spread and used. Therefore, the development of algorithms for the efficient computation of the CP decomposition is ...
Advanced tensor based signal processing techniques for wireless communication systems and biomedical signal processing
Naskovska, Kristina (author) / Haardt, Martin / Almeida, André L.F. de / Haueisen, Jens
2020-01-28
Theses
Electronic Resource
English
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