Time-domain diffuse optical tomography processing by using the Mellin–Laplace transform

Abstract

We investigate the use of the Mellin-Laplace transform for reconstructing optical parameters from time-resolved optical tomography in diffusive media. We present here its definition, its mathematical properties, and its sensitivity to variations of optical properties. The method was validated on two-dimensional reconstructions from simulation in the reflection geometry. We conclude that reconstructions based on the Mellin-Laplace transform are more robust to noise than the methods using first moments.

Time-resolved diffuse optical tomography using fast-gated single-photon avalanche diodes

“…The reconstruction method is fully described in [18,28]. The image reconstruction is done in 2D within the plane (x, z) of Fig.…”

“…The used datatype is the Mellin-Laplace transform (MLT), enabling time-windowing of the TPSF [16,18] …”

“…We consider the stabilization of the depth of the reconstructed absorbing inclusion as convergence, which is reached in less than 10 iterations for all tested cases. All the details of the reconstruction method are documented in [18] for theoretical material on the MLT and in [28] for using this algorithm to process experimental signals.…”

“…When the full TPSF with fine time sampling is available, methods based on moments [16,17] or MellinLaplace transforms [18] can be used to reconstruct maps of µ a or µ s ' coefficients in the medium. These methods have the main advantage of requiring limited calculation steps and therefore limited processing time.…”

Chromophore decomposition in multispectral time-resolved diffuse optical tomography

“…The algorithm is based on the time-domain diffusion equation which is solved by MellinLaplace transform [28]. To linearize the inverse problem, we used a "Born approximation" perturbation approach which also permits to eliminate the instrument response function (IRF) in our reconstruction algorithm.…”