FMRI UNMIXING VIA PROPERLY ADJUSTED DICTIONARY LEARNING Yannis Kopsinis 1 Harris Georgiou 1 Sergios Theodoridis 1 1 University of Athens Dept. Informatics & Telecomms., Athens, Greece Emails: kopsinis@ieee.org, xgeorgio@di.uoa.gr, stheodor@di.uoa.gr ABSTRACT The mapping of the functional networks within the brain is a major step towards a deeper understanding of the the brain function. It involves the blind source separation of obtained fMRI data, usually performed via independent component analysis (ICA). Recently, there is an increased interest for al- ternatives to ICA for data-driven fMRI unmixing and notably good results have been attained with Dictionary Learning (DL) - based analysis. In this paper, the K-SVD DL method is appropriately adjusted in order to cope with the special properties characterizing the fMRI data. Index Terms— Matrix Factorization, fMRI, Blind Source Separation, Dictionary Learning 1. INTRODUCTION Functional Magnetic Resonance Imaging (fMRI) [1] is a powerful non-invasive tool for localizing and analyzing brain activity. Most commonly it is based on blood oxygena- tion level-dependent (BOLD) contrast, which translates to detecting localized changes in the hemodynamic flow of oxygenated blood in activated brain areas. This is achieved by exploiting the different magnetic properties of oxygen- saturated versus oxygen-desaturated hemoglobin. In the brain, tasks involving action, perception, cogni- tion, etc., are performed via the simultaneous activation of a number of functional brain networks (FBN), which are en- gaged in proper interactions in order to effectively execute the task. Such networks are usually related to low-level brain functions and they are defined as a number of segregated spe- cialized small brain regions, potentially distributed over the whole brain. These regions collaborate in order to coherently perform a certain brain function [2]. The segregated brain regions involved in a certain brain network are said to be in- tegrated, [2], in the sense that irrespective of their anatom- ical proximity or remoteness, they exhibit strong anatomi- cal and/or functional connectivity. Functional connectivity is often expressed as strong coherence in the activation time- patterns of these regions. Examples of such brain networks are the visual, sensorimotor, auditory, default-mode, dorsal attention, and executive control networks. This work is partly supported by Marie Curie IEF, “SOL”, 302898 and by the NSRF programme, ARISTEIA ASSURANCE, co-funded by the EU and the Greek State. A challenging fMRI experimental procedure is the task- free one, referred to as resting-state fMRI. In this case, there is no correlation to previously known activation patterns, in- duced by external stimulus to the subject, and, hence, the steady-state functional analysis of the brain activity needs to be realized blindly. Independent Component Analysis (ICA) [3], which searches for functionally independent components or “sources” in the recorded fMRI signal is the most com- monly used method in this case. Recently, there is an increased interest for alternatives to ICA for data-driven fMRI unmixing. Notably good results have been attained with Dictionary Learning (DL) - based fMRI analysis, which can be grouped in two major categories. Those dealing with the analysis of the fMRI data of a single subject (e.g. of a certain person)[4, 5] and those that jointly accommodate data of multiple subjects, e.g.,[6–8]. In a dif- ferent approach [9], DL was applied not on the data matrix itself but on correlations between columns of Y correspond- ing to carefully selected Regions of Interest (ROIs). In this paper, we focus on the single subject case and particularly to DL based on the popular K-SVD (K-Singular Value Decom- position) method [10,11]. The K-SVD is properly modified in order to be rendered suitable for the analysis of fMRI data. In particular, a mechanism for the detection and effective joining of FBNs which are incorrectly split by conventional K-SVD is proposed in order to comply with the segregation and inte- gration properties of the FBN. Moreover, extra care is given in order to cope well with machine artifacts. 2. PROBLEM DESCRIPTION The data is collected during an fMRI experiment from suc- cessive 3D brain volume scans. Relying on adequate post- processing, which effectively compensates for possible time- lags [1], it is fairly accurate to assume that each acquisition is performed instantly. Therefore, the outcome of each scan, is a number of, say n, values, quantifying the activation at n points across the brain, at a certain time instance, say i. These points (voxels) are spatially distributed on a 3D grid and their values are collected in vector y i ∈ R n . Such vectors are also referred to as spatial maps. Considering t successive acquisitions, the full amount of data is collected in a matrix Y =[y T 1 , y T 2 ,..., y T t ] T ∈ R t×n . Hereafter, the notations, Y i,· and Y ·,j are used to denote the ith and the j th row and column respectively. Moreover, Y I,J , is the submatrix of Y