header for SPIE use Comparison of linear reconstruction techniques for 3D DPDW imaging of absorption coefficient Richard J. Gaudette a. , David A. Boas b , Dana H. Brooks a , Charles A. DiMarzio a , Misha E. Kilmer a , Eric L. Miller a a Department of Electrical and Computer Engineering, Northeastern University, Boston, MA. 02115 b NMR Center, Massachusetts General Hospital, Charlestown, MA and Electro-Optics Technology Center, Tufts University, Medford, MA In this paper we examine the performance of a number of linear techniques for reconstructing the 3-D distribution of absorption coefficient within a highly scattering medium using the diffuse photon density wave (DPDW) approximation. The simulation consists of a coplanar array of sources and detectors at the boundary of an infinite slab medium. The primary difficulty in the linear reconstruction of the 3D volume from a 2D array of measurement is that the forward matrix is both underdetermined and ill-conditioned. With a typical measurement geometry the system is underdetermined because we are trying to estimate absorption coefficient of about eight times as many voxels as we have measurements. Additionally, the forward matrix used to reconstruct the volume is ill-conditioned due to the source-detector geometry and the fact that the imaging volume is within the near field of the array. This results in neighboring source-detector pairs containing very similar information or equivalently, small angles between the row spaces of the forward matrix. Thus when attempting to “invert” this matrix we not only have to be concerned with the underdetermined nature of the inverse system but also with the wide range of singular values and their effect on the reconstruction. The techniques we examined included the algebraic techniques ART and SIRT and subspace techniques based on the singular value decomposition (TSVD) and the truncated conjugate gradient algorithm (TCG). The results show that the performance of the subspace techniques is superior to the algebraic techniques in localization of inhomogeneities, estimation of their amplitude and over image fidelity. Keywords: Photon density wave imaging, volumetric reconstruction, linear methods, inverse problems 1. INTRODUCTION Over the past ten years there has been considerable research into the use of near infrared light to image inside the human body, known as Diffuse Photon Density Wave (DPDW) imaging. One of the primary goals of this research is to image the distribution of the optical absorption coefficient, which at near infrared wavelengths (700-900 nm) is primarily due to hemoglobin in its various forms. Thus a mapping of the density of hemoglobin can be inferred from an image of the absorption coefficient. A number of approaches have been developed to image the absorption coefficient. These include linear, nonlinear, and backpropagation techniques. Nonlinear techniques such as those developed by Arridge et al. 1 , and Jiang et al. 2 , are attractive because they minimize the number of assumptions regarding both the medium and the physics of the problem, but they are computationally very expensive. Backpropagation, which has been explored by groups such as Colak et al. 3 and Matson et al. 4 , is computationally economical but sensitive to noise and does not deal well with multiple absorbing objects. Linear perturbation techniques attempt specify the imaging problem as a perturbation to a known or estimated background medium and pose the relationship between the absorption coefficient and the measured data as a linear system of equations. Linear methods include both the Born and Rytov approximations and have been explored by O'Leary et al. 5 and Chang et al. 6 , among others. In this paper we present a performance comparison of several of the more commonly employed absorption imaging techniques based on the linear perturbation approach. This work differs from most previous investigations into linear reconstruction techniques in that we reconstruct the full three dimensional absorption function instead of just a single plane in the volume. Specifically, we examine the performance of two classes of 3D reconstruction techniques, algebraic . Other author information: RJG: rjg@cdsp.neu.edu, DAB: dboas@nmr.mgh.harvard.edu, DHB: brooks@cdsp.neu.edu, CAD: cdimarzio@lynx.dac.neu.edu, MEK: mkilmer@ece.neu.edu, ELM: elmiller@cdsp.neu.edu This work was supported by the Northeastern University Presidents Fund, Army Research Office Demining MURI under Grant DAAG55-97-1-0013 and the NSF.