Sampling and reconstruction schemes for biomagnetic sensor arrays

In this paper we generalize the approach of Ahonen et al (1993 IEEE Trans. Biomed. Eng. 40 859-69) to two-dimensional non-uniform sampling. The focus is on two main topics: (1) searching for the optimal sensor configuration on a planar measurement surface; and (2) reconstructing the magnetic field (a continuous function) from a discrete set of data points recorded with a finite number of sensors. A reconstruction formula for Bz is derived in the framework of the multidimensional Papoulis generalized sampling expansion (Papoulis A 1977 IEEE Trans. Circuits Syst. 24 652-4, Cheung K F 1993 Advanced Topics in Shannon Sampling and Interpolation Theory (New York: Springer) pp 85-119) in a particular case. Application of these considerations to the design of biomagnetic sensor arrays is also discussed.