Hs. Oster et Y. Rudy, REGIONAL REGULARIZATION OF THE ELECTROCARDIOGRAPHIC INVERSE PROBLEM -A MODEL STUDY USING SPHERICAL GEOMETRY, IEEE transactions on biomedical engineering, 44(2), 1997, pp. 188-199
This study examines the use of a new regularization scheme, called reg
ional regularization, for solving the electrocardiographic inverse pro
blem. Previous work has shown that different time frames in the cardia
c cycle require varying degrees of regularization, This reflects diffe
rences in potential magnitudes, gradients, signal-to-noise ratio (SNR)
, and locations of electrical activity, One might expect, therefore, t
hat a single regularization parameter and a uniform level of regulariz
ation may also be insufficient for a single potential map of a single
time frame because in one map there are regions of high and tow potent
ials and potential gradients, Regional regularization is a class of me
thods that subdivides a given potential map into functional ''regions'
' based on the spatial characteristics of the potential (''spatial fre
quencies''), These individual regions are regularized separately and r
ecombined into a complete map, This paper examines the hypothesis that
such regionally regularized maps are more accurate than if all region
s were taken together and solved with an averaged level of regularizat
ion, In a homogeneous concentric spheres model, Legendre polynomials a
re used to decompose a torso potential map into a set of submaps, each
with a different degree of spatial variation, The original torso map
is contaminated with data noise, or geometrical error or both, and reg
ional regularization improves the epicardial potential reconstruction
by up to 25% [relative error (RE)], Regional regularization also impro
ves the reconstructed location of peaks. A practical goal is to extend
the application of this method to the realistic torso geometry, but b
ecause Legendre decomposition is limited to geometries with spherical
symmetry, other methods of map decomposition must be found, Singular v
alue decomposition (SVD) is used to decompose the maps into component
parts, Its individual submaps also have different levels of spatial va
riation; moreover, it is generalizable to any vector, does not require
spherical symmetry, and is extremely efficient numerically, Using SVD
decomposition for regional regularization, significant improvement wa
s achieved in the map quality in the presence of data noise.