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We compared the performance of a channelized Hotelling observer (CHO) to that of human observers to determine an optimal smoothing parameter β for an SKE/BKE detection task in a SPECT MAP (maximum a posteriori) reconstruction. The study is motivated in part by the recent development of theoretical methods that can rapidly predict CHO signal-to-noise ratios (SNRs) for MAP reconstructions. We found that a CHO not adjusted for internal noise effects was less predictive of the optimal smoothing parameters than one that used human observer data to tune the CHO for internal noise. We used a three-channel, square profile, radially symmetric channel structure, and, for internal noise, a method that altered the diagonal elements of the channel covariance matrix. The human observer study for two different signals A and B showed that β in the range 0.5-10.0 produced high detectability as measured by high dA2, while the CHO without internal noise showed high SNR2 for β in the wider range 0.01-10.0. The CHO at location A was modified by internal noise utilizing human data at A, so that the dA2 and SNR2 overlapped well, but when these internal noise parameters from A were applied at B, the curves did not overlap well. Nevertheless, both modified CHOs predicted a β range in accord with human data. We conclude that CHOs may need some way of incorporating internal noise without having to conduct a human study in the first place to determine internal noise parameters.