Task-based assessment of image quality (IQ) is critically important for the design and optimization of medical imaging systems. Ideal observers, including the Bayesian Ideal Observer (IO) and the ideal linear observer, i.e., the Hotelling observer (HO), provide objective figures of merit (FOMs) that quantify system performance on signal detection tasks. However, the application of ideal observers to high-dimensional image data is often computationally intractable. Channel mechanisms provide an effective framework for dimensionality reduction that can facilitate the computation of ideal observers. This work presents a conjugate gradient (CG)-based method to construct efficient channels for approximating the IO and HO performance.