A new method is proposed for activation detection in event-related functional magnetic resonance imaging (fMRI). The method is based on the analysis of selected resolution levels (a subspace) in translation invariant wavelet transform (TIWT) domain. Using a priori knowledge about the activation signal and trends, we analyze their power in different resolution levels in TIWT domain and select an optimal set of resolution levels. A randomization-based statistical test is then applied in the wavelet domain for activation detection. This approach suppresses the effects of trends and enhances the detection sensitivity. In addition, since TIWT is insensitive to signal translations, the power analysis is robust with respect to signal shifts. The randomization test alleviates the need for assumptions about fMRI noise. The method has been applied to simulated and experimental fMRI datasets. Comparisons have been made between the results of the proposed method, a similar method in the time domain and the cross-correlation method. The proposed method has shown superior sensitivity compared to the other methods.