In neuromagnetic source reconstruction, a functional map of neural activity is constructed from noninvasive magnetoencephalographic (MEG) measurements. The overall reconstruction problem is under-determined, so some form of source modeling must be applied. The authors review the two main classes of reconstruction techniques-parametric current dipole models and nonparametric distributed source reconstructions. Current dipole reconstructions use a physically plausible source model, but are limited to cases in which the neural currents are expected to be highly sparse and localized. Distributed source reconstructions can be applied to a wider variety of cases, but must incorporate an implicit source model in order to arrive at a single reconstruction. The authors examine distributed source reconstruction in a Bayesian framework to highlight the implicit nonphysical Gaussian assumptions of minimum norm based reconstruction algorithms. They conclude with a brief discussion of alternative non-Gaussian approaches.

The most widely used model for electroencephalography (EEG) and magnetoencephalography (MEG) assumes a quasi-static approximation of Maxwell's equations and a piecewise homogeneous conductor model. Both models contain an incremental field element that linearly relates an incremental source element (current dipole) to the field or voltage at a distant point. The explicit form of the field element is dependent on the head modeling assumptions and sensor configuration. Proper characterization of this incremental element is crucial to the inverse problem. The field element can be partitioned into the product of a vector dependent on sensor characteristics and a matrix kernel dependent only on head modeling assumptions. The authors present the matrix kernels for the general boundary element model (BEM) and for MEG spherical models. They show how these kernels are easily interchanged in a linear algebraic framework that includes sensor specifics such as orientation and gradiometer configuration. They then describe how this kernel is easily applied to "gain" or "transfer" matrices used in multiple dipole and source imaging models.

Neuromagnetic source reconstruction is the process of deducing internal brain currents from the external magnetic fields they produce. Brain currents are the result of neural activity and a map of their distribution corresponds to a functional image of the brain. In this paper the reconstruction is formulated as an underdetermined linear inverse problem to which a minimal source solution is sought. The minimal source solution is defined by the minimization of a hybrid metric that accounts for both the sparseness of the reconstruction and its compatibility with the measured magnetic field. Genetic algorithms are employed as a robust means of computing this minimal source reconstruction.>

A systolic array design for the algebraic path problem (APP) is presented that is both simpler and more efficient than previously proposed configurations. This array uses N/sup 2/ orthogonally connected processing elements and requires 2N I/O connections. Total computation time is 5N-2, which is the minimum time possible in a systolic implementation. The data pipelining rate is one, so no pipeline interleave is required. For multiple problem instances a block pipeline rate of N can be achieved, which is optimal for an array of N/sup 2/ processing elements.>

Neural networks are examined in the context of function approximation and the related field of time series prediction. A natural extension of radial basis nets is introduced. It is found that use of an adaptable gradient and normalized basis functions can significantly reduce the amount of data necessary to train the net while maintaining the speed advantage of a net that is linear in the weights. The local nature of the network permits the use of simple learning algorithms with short memories of earlier training data. In particular, it is shown that a one-dimensional Newton method is quite fast and reasonably accurate

A time-varying spatial/temporal filter for enhancing multichannel magnetoencephalographic (MEG) recordings of evoked responses is described. The filter is based on projections derived from a combination of measured data and a priori models of the expected response. It produces estimates of the evoked fields in single-trial measurements. The estimates can reduce the need for signal averaging in some situations. The filter uses the a priori model information to enhance responses where they exist, but avoids creating responses that do not exist. Examples are included of the filter's application to both MEG single-trial data containing an auditory evoked field and control data with no evoked field.>

A multichannel adaptive lattice algorithm is derived that provides a least-squares estimate of a primary signal in terms of the last p samples of m reference signals. The recursions developed are optimized for multichannel use and provide an algorithm with computational complexity O(pm/sup 2/). In the single reference channel case (m=1), the algorithm simplifies to the O(p) least-squares lattice (LSL) algorithm. In the single filter tap case (p=1), the algorithm simplifies to the O(m/sup 2/) 'Kalman' recursive least-squares (RLS) algorithm. Hence, the general multichannel least-squares lattice (MLSL) presented provides an explicit relationship between, and common derivation of, both the LSL and RLS algorithms.>

An algorithm and a set of array architectures that implement and multichannel adaptive least squares lattice filter are presented. The algorithm is based on QR decomposition and provides both a numerically sound and regularly structured set of recursions. For m channels and p filter taps, O(pm/sup 2/) computations are required at each sample update. Several array architectures are presented to illustrate the space-time tradeoffs available. These range from an array of p processing elements (PEs) that compute a sample update in O(m/sup 2/) time to an array of O(pm/sup 2/) PEs that computes the update in constant time. The in-between arrays of O(m), O(m/sup 2/), or O(pm) PEs are also outlined.>

Due to VLSI technological progress, algorithm- oriented array architectures, such as systolic arrays, appear to be very effective, feasible, and economic. This paper discusses how to design systolic arrays for the transitive closure and the shortest path problems. We shall focus on the Warshall algorithm for the transitive closure problem and the Floyd algorithm for the shortest path problem. These two algorithms share exactly the same structural formulation; therefore, they lead to the same systolic array design. In this paper, we first present a general method for mapping algorithms to systolic arrays. Using this methodology, two new systolic designs for the Warshall-Floyd algorithm will be derived. The first one is a spiral array, which is easy to derive and can be further simplified to a hexagonal array. The other is an orthogonal systolic array which is optimal in terms of pipelining rate, block pipelining rate, and the number of input/output connections.