We describe a comprehensive linear approach to the prob- lem of imaging brain activity with high temporal as well as spatial resolution based on combining EEG and MEG data with anatomical constraints derived from MRI images. The "inverse problem" of estimating the distribution of dipole strengths over the conical surface is highly nnderdetermined, even given closely spaced EEG and MEG recordings. ',x.'c h:,vc obtained much better solutions to this problem by explicitly incorporating both local cortical orientation as well as spatial covariance of sources and sensors into our formulation. ;m explicit polygonal model of the cortical manifold is first constructed :,s follows: (1) slice data in three onhogon;,l pJ:,ncs of section (needle-shaped voxels) are combined with a linear aleblurring technique to make a single high.resolution 3-D image (cubic voxels), (2) the image is recursively fiood4illed ,o determine the topology of the gray.white matter border, and (3) the resulting continuous surface is refinc by relaxing it against the original 3-D gray-scale image using a deformable template method, which is also used to computationally flatten the cortex for k'asier vic'ing. The explici solution to an error minimi- zAti(m tbvmulation of an optimal inverse linear operator (for a paicular ct)ical manilbld, sensor placement, noise and prior source covariance) gives rise to a compact expression that is practically computahle for hundreds of sensors and thousan& of sources, The inverse solution can then l weighted for a particular (averaged) event using the sensor cox=riance for that evt'nt. Model studies surest that we m% be able to localize muhiple conical sources with spatial relution as good as PET with this technklue, while retaining a much finer grain picture of activity ov...