Abstract-In this paper, we discuss several aspects of a potential new medical imaging modality for producing a quantitative three-dimensional map of neuron current densities associated with brain function. The neuromagnetic image is produced by reconstructing a current dipole field from external magnetic field measurements made with an array of superconducting quantum interference device (SQUID) [3]. These data have been used to estimate the location, orientation, and magnitude of a single current dipole in the brain which best fits the data in a least squares sense [1], [4], [5]. This approach is useful when the current field of interest is known to be localized to a single small region of the brain. Neuromagnetic imaging extends this concept to the case of multiple-current dipole sources or more complex distributed current fields which would exist when separated regions of the brain are involved in a response, or during higher brain functions. In these cases, the single-dipole model is a poor match [5], [6] and we are motivated to treat the problem as one of image reconstruction. Our approach then emphasizes solutions to the inverse problem (current field from magnetic measurements) using image reconstruction algorithms and techniques which one might encounter in computed tomography or other medical imaging applications.Neuromagnetic imaging on a single reconstruction plane in the brain was first demonstrated by Singh et al. [7]. Their approach used discrete samples of the evoked magnetic field to reconstruct a current field modeled as discrete current dipole cells all lying in a single plane with either one-or two-constrained dipole orientations. The depth of this single plane was adjusted for best fit with the measured data. We propose an extension to this model which will include three-dimensional reconstructed images and multiple-dipole orientations. This allows the estimation of dipole distributions in depth as well as lateral position and orientation.The paper is organized as follows. In Section II, we introduce the basic physical model we will use for NMI and develop the mathematical formulation of this model. We then discuss possible constraints on the solution and how these may be included in the formulation. In Section III, the fundamental limits on image resolution due to background noise, the SQUID response, and the ill-conditioned nature of the system matrix are discussed. In Section IV, we present several algorithms which can be applied to the NMI reconstruction problem and evaluate their effectiveness. Results of computer model evaluation of these algorithms are also included.