A novel method for iterative reconstruction of images from undersampled MRI data acquired by multiple receiver coil systems is presented. Based on Projection onto Convex Sets (POCS) formalism, the method for SENSitivity Encoded data reconstruction (POCSENSE) can be readily modified to include various linear and nonlinear reconstruction constraints. Such constraints may be beneficial for reconstructing highly and overcritically undersampled data sets to improve image quality. POCSENSE is conceptually simple and numerically efficient and can reconstruct images from data sampled on arbitrary k-space trajectories. The applicability of POCSENSE for image reconstruction with nonlinear constraining was demonstrated using a wide range of simulated and real MRI data.

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We present the "Near Optimal IsoSurface Extraction" (NOISE) algorithm for rapidly extracting isosurfaces from structured and unstructured grids. Using the span space, a new representation of the underlying domain, we develop an isosurface extraction algorithm with a worst case complexity of o(& + c) for the search phase, where n is the size of the data set and k is the number of cells intersected by the isosurface. The memory requirement is kept at O(n) while the preprocessing step is O(n log n). We utilize the span space representation as a tool for comparing isosurface extraction methods on structured and unstructured grids. We also present a fast triangulation scheme for generating and displaying unstructured tetrahedral grids.

In recent years, significant progress has been made in the area of electroencephalography (EEG) source imaging. Source localization on simple spherical models has become increasingly efficient, with consistently reported accuracy of within 5 mm. In contrast, source localization on realistic head models remains slow, with subcentimeter accuracy being the exception rather than the norm. A primary reason for this discrepancy is that most source imaging techniques are based on lead fields. While the lead field for simplified geometries can be easily computed analytically, an efficient method for computing realistic domain lead fields has, until now, remained elusive. In this paper, we propose two efficient methods for computing realistic EEG lead-field bases: the first is element oriented and the second is node oriented. We compare these two bases, discuss how they can be used to apply recent source imaging methods to realistic models, and report timings for constructing the bases.

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