**LORETA / sLORETA / eLORETA**

LORETA: low resolution electromagnetic tomography (1993, 1994)

**s**LORETA:
**standardized** low resolution
electromagnetic tomography (2002)

**e**LORETA:
**exact** low resolution
electromagnetic tomography (2007,
2011)

Comparing sLORETA and eLORETA to almost all other 3D discrete linear tomographies from the literature (2018)

**
Old
LORETA homepage for lots of information**

**
Recent LORETA homepage,
loaded with information**

**Why LORETA? **
**Quantitative analyses of brain electric activity rely on the development
of innovative models and methods that must minimally satisfy, if possible, two
criteria:**

**(1) Validation, if experimental ground truth is available.**

**(2) Best performance, based on fair, objective comparisons to other
similar published methods, using simulations.**

These methods deal with the EEG/MEG neuroimaging problem: given measurements of scalp electric potential differences (EEG: electroencephalogram) and extracranial magnetic fields (MEG: magnetoencephalogram), find the 3D distribution of the generating electric neuronal activity.

Consider the family of linear 3D distributed inverse solutions. And consider the localization error to a point test source anywhere in the solution space. Then, an inverse solution is unreliable if it has localization error to point sources. In other words, an inverse solution is unreliable if it has localization bias.

This is very important, since imaging is all about localization. Mislocalization is unacceptable.

LORETA (1993, 1994) has localization bias, albeit small.

sLORETA and eLORETA have zero localization error to point sources.

Here is a comparison of a large family of linear inverse solutions: https://doi.org/10.1101/269753

The abstract for the comparative study follows:

EEG/MEG neuroimaging consists of estimating the cortical distribution of time
varying signals of electric neuronal activity, for the study of functional
localization and connectivity. Currently, many different imaging methods are
being used, with very different capabilities of correct localization of activity
and of correct localization of connectivity. The aim here is to provide a
guideline for choosing the best (i.e. least bad) imaging method. This first
study is limited to the comparison of the following methods for EEG signals:
sLORETA and eLORETA (standardized and exact low resolution electromagnetic
tomography), MNE (minimum norm estimate), dSPM (dynamic statistical parametric
mapping), and LCMVBs (linearly constrained minimum variance beamformers). These
methods are linear, except for the LCMVBs that make use of the quadratic EEG
covariances. To achieve a fair comparison, it is assumed here that the
generators are independent and widely distributed (i.e. not few in number),
giving a well-defined theoretical population EEG covariance matrix for use with
the LCMVBs. Measures of localization error, false positive activity, and false
positive connectivity are defined and computed under ideal no-noise conditions.**
It is empirically shown with extensive simulations that: (1) MNE, dSPM, and all
LCMVBs are in general incapable of correct localization, while sLORETA and
eLORETA have exact (zero-error) localization; (2) the brain volume with false
positive activity is significantly larger for MN, dSPM, and all LCMVBs, as
compared to sLORETA and eLORETA; and (3) the number of false positive
connections is significantly larger for MN, dSPM, all LCMVBs, and sLORETA, as
compared to eLORETA.** Non-vague and fully detailed equations are
given. PASCAL program codes and data files are available. It is noted that the
results reported here do not apply to the LCMVBs based on EEG covariance
matrices generated from extremely few generators, such as only one or two
independent point sources.