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The inverse signal-to-noise ratio (SNR) problem is defined as determining the average SNR X required to achieve a specified probability of detection Pd, given Pfa the false alarm probability, N the integration number, and K a target fluctuation parameter that encompasses the Swerling and Marcum models. Although exact expressions exist for the standard problem of determining Pd given X and the other parameters, these expressions cannot be inverted. We present here approximations for the required SNR over a wide range of parameter values. Over most of the specified parameter ranges, the magnitude of the error in these approximations is less than 1 dB, in fact mostly less than 0.5 dB. If the resulting accuracy is insufficient, then an iterative procedure is necessary and the approximate value Xap' can be used as a starting value. The Marcum case results apply directly to the radiometry inverse problem as well.