Mathematical Methods in Interdisciplinary Sciences

15Brain Activity Reconstruction by Finding a Source Parameter in an Inverse Problem

Amir H. Hadian‐Rasanan¹ and Jamal Amani Rad²

¹Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Evin, Tehran, Iran

²Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Tehran, Iran

15.1 Introduction

Brain activity reconstruction is the field of studying and reconstructing human brain activities from imaging data such as functional magnetic resonance imaging (fMRI), electroencephalography (EEG), magnetoencephalography (MEG), and so on. This field of neuroscience has attracted a lot of attention recently and different tools and algorithms have been developed for this purpose. On the other hand, because deep learning methods obtained outperform results in different problems of science, some researchers employed these methods for their problems and found out that a good tool for reconstruction of the brain activities are deep learning methods. Despite the deep learning methods have good accuracy and are so useful, all of them have a major problem, which is considering the learning algorithm as a black box. Moreover, there is no meaningful way that can explain “Why do the employed deep learning methods get good results?”. Fortunately, this major problem can be solved by using a suitable mathematical model. There are various mathematical tools for modeling this phenomenon. One of the most useful mathematical models for this ...