Minimum-noise Laplacian kernel for MR-based electrical properties tomography

Noise amplification by Laplacian operation on a noisy input RF map is an important limiting factor in the SNR of MR-based electrical properties tomography (MREPT). We show that among all linear Laplacian kernels, the one based on the Savitzky-Golay second-order derivative kernel has the least amount of noise amplification. A method to construct such a kernel for an arbitrary three-dimensional ROI is presented, and its performance is compared with other Laplacian kernels used in literature.

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