# Spatial deconvolution technique to improve the accuracy of reconstructed three–dimensional diffuse optical tomographic images

### H. L. Graber *et al.* (2005)

#### Summary

A straightforward spatial deconvolution operation is presented that seeks to invert the information blurring
property of first-order perturbation algorithms for diffuse optical tomography (DOT) image
reconstruction. The method that was developed to generate these deconvolving operators, or filters, was
conceptually based on the frequency-encoding process used in magnetic resonance imaging. The computation
of an image-correcting filter involves the solution of a large system of linear equations, in which
known true distributions and the corresponding recovered distributions are compared. Conversely,
application of a filter involves only a simple matrix multiplication. Simulation results show that application
of this deconvolution operation to three-dimensional DOT images reconstructed by the solution of
a first-order perturbation equation (Born approximation) can yield marked enhancement of image quality.
In the examples considered, use of image-correcting filters produces obvious improvements in image
quality, in terms of both location and *m*_{a} of the inclusions. The displacements between the true and
recovered locations of an inclusion’s centroid location are as small as 1 mm, in an 8.cm-diameter medium
with 1.5.cm-diameter inclusions, and the peak value of the recovered *m*_{a} for the inclusions deviates from
the true value by as little as 5%.