In OFDM relay networks with IQ imbalances and full-duplex relay station (RS), how to optimize pilot pattern and power allocation using the criterion of minimizing the sum of mean square errors (Sum-MSE) for the frequency-domain least-squares channel estimator has a heavy impact on self-interference cancellation. Firstly, the design problem of pilot pattern is casted as a convex optimization. From the KKT conditions, the optimal analytical expression is derived given the fixed source power and RS power. Subsequently, an optimal power allocation (OPA) strategy is proposed and presented to further alleviate the effect of Sum-MSE under the total transmit power sum constraint of source node and RS. Simulation results show that the proposed OPA performs better than equal power allocation (EPA) in terms of Sum-MSE, and the Sum-MSE performance gain grows with deviating $ρ$ from the value of $ρ^o$ minimizing the Sum-MSE, where $ρ$ is defined as the average ratio of the residual SI channel at RS to the intended channel from source to RS. For example, the OPA achieves about 5dB SNR gain over EPA by shrinking or stretching $ρ$ with a factor $4$. More importantly, as $ρ$ decreases or increases more, the performance gain becomes more significant.