tensor decomposition

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.

One of the most well-known multimodality techniques is the integration of EEG and fMRI datasets. Convolution of EEG signals with hemodynamic response function is one of the most important methods to consider the effect of HRF in the fusion of EEG and fMRI data. However, the latencies and amplitudes of ERPs and fMRI spatial components are affected by the low pass filtering effect of HRF in each trial. In this paper, we have proposed a new method based on Advanced Coupled Matrix Tensor Factorization model to jointly factorize the EEG tensor and fMRI matrix while we simultaneously remove the effect of HRF through decomposition of fMRI dataset. Applying the proposed method to an auditory oddball paradigm of simultaneous EEG-fMRI recording, the well-known ERP of oddball paradigm and the corresponding fMRI spatial maps are estimated. The results demonstrate that our proposed approach is strongly capable of extracting the ERPs and their corresponding fMRI spatial components, while simultaneously estimates the trial to trial variations of these factors with accurate amplitude and latency in each trial.