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This work investigates the design of optimum distribution of photon density power among the source positions, and modulation frequencies to maximize the detectability of heterogeneities in near-infrared diffuse optical to- mography. We start our analysis by first deriving the discrete source-to-detector map based on the finite-element formulation of the frequency-domain diffusion equation with Robin boundary conditions. We formulate the detection of heterogeneities with respect to a given background as a hypothesis testing problem and use signal- to-noise ratio (SNR) of the test statistics as a figure of merit for detectability. We, next, maximize the SNR of the test statistics with respect to the source power distributed over a predetermined set of locations and frequen- cies. When the optimal linear detector is used for detection, optimal source power distribution is given as the maximum eigenfunction of the source-to-detector map normalized with respect to the covariance of measurement noise. We present numerical studies to demonstrate the performance of our approach with respect to number of source locations, tumor size, and tumor location.

Optimum source design for detection of heterogeneities in diffuse optical imaging