Tensor Methods in Biomedical Image Analysis

Abstract

Abstract
In the past decade, tensors have become increasingly attractive in different aspects of signal and
image processing areas. The main reason is the inefficiency of matrices in representing and analyzing
multimodal and multidimensional datasets. Matrices cannot preserve the multidimensional correlation
of elements in higher?order datasets and this highly reduces the effectiveness of matrix?based
approaches in analyzing multidimensional datasets. Besides this, tensor?based approaches have
demonstrated promising performances. These together, encouraged researchers to move from matrices
to tensors. Among different signal and image processing applications, analyzing biomedical signals
and images is of particular importance. This is due to the need for extracting accurate information
from biomedical datasets which directly affects patient’s health. In addition, in many cases, several
datasets have been recorded simultaneously from a patient. A common example is recording
electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) of a patient with
schizophrenia. In such a situation, tensors seem to be among the most effective methods for the
simultaneous exploitation of two (or more) datasets. Therefore, several tensor?based methods have
been developed for analyzing biomedical datasets. Considering this reality, in this paper, we aim to
have a comprehensive review on tensor?based methods in biomedical image analysis. The presented
study and classification between different methods and applications can show the importance of
tensors in biomedical image enhancement and open new ways for future studies.