Task-based measures of image quality (IQ) quantify the ability of an observer to perform a specific task. Such measures are employed for assessing and optimizing medical imaging systems. Although the Bayesian ideal observer is optimal by definition, it is frequently both non-linear and intractable. In such cases, linear observers are commonly employed. However, the optimal linear observer, the Hotelling observer (HO), becomes intractable when considering large images. Channelized methods have become popular for reducing the dimensionality of image data. In this work, we propose a novel method for determining efficient channels by learning them with autoencoders (AEs). Autoencoders are neural networks that can be employed to learn concise representations of data, frequently for the purposes of reducing dimensionality. We trained several AEs to encode task-specific information by modifying the standard loss function and examined the effect of hidden layer size and the use of tied/untied weights on the resulting representation accuracy. Subsequently, HOs were applied to both the original images and the dimensionality-reduced versions of them produced by the AEs. It was demonstrated that, for a suitable specification of the AE, the performance of the HO was relatively unaffected by the encoding of the image. However, the computational cost of inverting the covariance matrix was greatly reduced when the HO was applied with the encoded data due to its reduced dimensionality. Our findings suggest that AEs may represent an attractive alternative to the use of heuristic channels for reducing the dimensionality of image data when seeking to accurately approximate the performance of the HO on signal detection tasks.