A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient.

We compare, through simulations, the performance of four linear algorithms for diffuse optical tomographic reconstruction of the three-dimensional distribution of absorption coefficient within a highly scattering medium using the diffuse photon density wave approximation. The simulation geometry consisted of a coplanar array of sources and detectors at the boundary of a half-space medium. The forward solution matrix is both underdetermined, because we estimate many more absorption coefficient voxels than we have measurements, and ill-conditioned, due to the ill-posedness of the inverse problem. We compare two algebraic techniques, ART and SIRT, and two subspace techniques, the truncated SVD and CG algorithms. We compare three-dimensional reconstructions with two-dimensional reconstructions which assume all inhomogeneities are confined to a known horizontal slab, and we consider two 'object-based' error metrics in addition to mean square reconstruction error. We include a comparison using simulated data generated using a different FDFD method with the same inversion algorithms to indicate how our conclusions are affected in a somewhat more realistic scenario. Our results show that the subspace techniques are superior to the algebraic techniques in localization of inhomogeneities and estimation of their amplitude, that two-dimensional reconstructions are sensitive to underestimation of the object depth, and that an error measure based on a location parameter can be a useful complement to mean squared error.

Temporal and spatial analysis of potential maps via multiresolution decompositions.

Cardiac potentials recorded on the epicardium or the body surface by an array of electrodes are usually analyzed either as spatial distributions or temporal waveforms. Thus, the analysis often involves temporal descriptors (eg. max dV/dt) or spatial descriptors (eg. location of local extrema) only. The best known transform technique that has been applied to these data that combines both spatial and temporal characteristics is the Karhunen-Loeve transform, a global transform applied to temporal and/or spatial bases obtained by statistical analysis of a database. As an alternative, multiresolution decompositions and related wavelet-type transforms have recently seen great development in signal processing and related fields. They offer flexibility, employing transformations onto local (rather than global) and fixed (rather than data-dependent) databases, and allow transformation of distributions, waveforms, or both, as desired. The utility of this method as applied to temporal and spatial segmentation and analysis of map data from both epicardial plaques and body surface potentials recorded during percutaneous transluminal coronary angioplasty is illustrated.