Introduction

Because of its direct sensitivity to hemodymanic processes, diffuse optical tomography (DOT) has shown great promise as a medical imaging modality for problems including breast tumor detection and functional brain imaging. A key challenge with DOT is the extraction of useful information about the relevant subsurface paramaters, optical absorption and scattering parameters, from fluence data measures at the body surface. In this regard, DOT requires the solution of a generally non-linear, ill-posed inverse problem. The intent of this Focus Issue of Optics Express is to accomplish two tasks. First, we want to highlight the current state-of-the-art in DOT inverse methods. Second, the similarity of the DOT problem to other inverse problems prompts us to include in this issue work from related endeavors. The overall goals then are to broaden the views of those working in DOT in terms of other approaches to their problems and to make the wider inverse problems community more aware of this exciting new area of work.

To this end, we have invited papers from some of the leading researchers in the area of diffuse inverse methods. The resulting collection represents the high caliber of work being done throughout the world on a number of basic issues related to such problems. The contributions center around four basic themes.

First, a key issue impacting DOT imaging is the choice of physical model to employ. While radiative transfer is the “exact” model, most DOT inverse methods are based on the more tractable diffusion approximation. The paper by Riley et al. explores the applicability of a diffusive model for three dimensional brain imaging applications where a clear, non-diffusive layer exists in the medium.

After having chosen a physical model, the second basic inversion issue is to determine what information one wishes to extract from the data. Rather than inverting for a large collection of pixels or voxels, there has been growing interest in using the sparse DOT data to determine a much smaller number of parameters describing the geometric structure of anomalies in the overall region of interest. The papers by Kolehmainen et al. and Kilmer et al. describe different shape-based approaches to the DOT inverse problem.

The third component in any inverse problem is the synthesis of an algorithm for extracting the desired information. Here we have two papers, one by Oliver Dorn and another by Hielscher et al., which examine issues related to the employment of radiative transfer models in inversion routines. These two papers offer an interesting contrast in the variety of ways such transport-based inversion schemes can be structured.

Finally, the paper by Nicolaides and Mandelis discusses current problems and proposed approaches for processing real sensor data. Specifically, they address issues related to the processing of data from thermal-wave diffraction tomographic microscopy, a non-destructive sensing modality whose underlying physics are essentially equivalent to diffusion-based DOT.

Eric Miller, Northeastern University