Tensor Methods in Biomedical Image Analysis

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.

Keywords: Biomedical image enhancement; tensor decomposition; tensor networks.

Figure 1

Some examples of biomedical images. From left to right, examples of an optical coherence tomography image and fundus fluorescein angiogram image

Figure 2

CANDECOMP/PARAFAC (first row) and Tucker (second row) decompositions of a 3^rd order tensor

Figure 3

Tensor train (first row) and tensor ring (second row) decompositions of an N^th order tensor

Figure 4

Matrix-tensor (first row) and tensor-tensor (second row) couplings of two datasets. The datasets are coupled along one mode

Figure 5

Hankelization of a vector. Using this method, a vector is transferred into a matrix with Hankel structure

Figure 6

Patch Hankelization of a matrix. Each square contains patch (blocks of elements) with size P × P

Figure 7

Comparison of reconstruction of a sample B-scan of dataset[14] with missing slices, using HaLRTC and MDT algorithms. The results show that HaLRTC (low-rank based approach using nuclear norm minimization) could not recover the missed slices, while MDT (decomposition based approach) could recover the image. PSNR and SSIM for each image have been reported beneath each image