Multiple efforts have been made in x-ray angiography to transition from traditional image quality metrics to mathematical observer models. Recent works have successfully implemented the channelized Hotelling observer (CHO) model for x-ray angiography systems. However, in these works the channel selection process is ambiguous and limits to identifying a range of frequencies and other channel parameters that are believed to represent the most relevant features of the imaging tasks. This channel selection rationale can be sufficient for certain simple scenarios but it might not be enough for more complex ones. On the other hand, it has been shown that besides dealing with the well-known bias caused by a finite number of samples, there is also another source of bias in the estimation of the detectability index in x-ray angiography. Such source of bias has been attributed to nonrandom differences in noise between images acquired at different time points, also referred as temporally variable nonstationary noise. This work proposes a task-specific automated method for optimal channel selection and corrects for the influence of bias due to temporally variable nonstationary noise, particular from x-ray angiography systems. The proposed method is computationally inexpensive, provides time efficient selection of optimal channels, and contributes to minimize bias, all of these without significantly compromising the accuracy of the detectability index estimation. This method for channel optimization can be readily adapted to other imaging modalities.