Psychoacoustic model based methods have recently been introduced in order to enhance speech signals corrupted by ambient noise. In particular, the perceptual filter is analytically derived where the frequency content of the input noisy signal is made the same as that of the estimated clean signal in auditory domain. However, the analytical derivation should rely on the deconvolution associated with the spreading function in the psychoacoustic model, which results in an ill-conditioned problem. In order to cope with the problem associated with the deconvolution, we propose a novel psychoacoustic model based speech enhancement filter whose principle is the same as the perceptual filter, however the filter is derived by a constrained optimization which provides solutions to the ill-conditioned problem. It is demonstrated with artificially generated signals that the proposed filter operates according to the principle. It is shown that superior performance results from the proposed filter over the perceptual filter provided that a clean speech signal is separable from noise.