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We show how a random matrix can be used to reduce the dimensionality of the bioluminescence tomography reconstruction problem. A randomised low-rank approximation for the sensitivity matrix is computed, and we show how this can be used to reconstruct the bioluminescence source distribution on a randomised basis for the mesh nodes. The distribution on the original mesh can be found easily via a simple matrix multiplication. The majority of the computation required can be performed in advance of the reconstruction, and the reconstruction time itself is of the order milliseconds. This could allow for high frame rate real-time reconstructions to be performed.

Random matrix-based dimensionality reduction for bioluminescence tomography reconstruction