Medical imaging systems are commonly assessed and optimized by use of objective measures of image quality (IQ). The performance of the Ideal Observer (IO) acting on imaging measurements has long been advocated as a figure-of-merit to guide the optimization of imaging systems. For computed imaging systems, the performance of the IO acting on imaging measurements also sets an upper bound on task-performance that no image reconstruction method can transcend. As such, estimation of IO performance can provide valuable guidance when designing data-acquisition techniques by enabling the identification of designs that will not permit the reconstruction of diagnostically useful images for a specified task-no matter how advanced the reconstruction method is or plausible the reconstructed images appear. The need for such analyses is urgent because of the ubiquitous development of deep learning-based image reconstruction methods and the fact that they are often not assessed by use of objective image quality measures. However, until recently, estimation of the IO was generally intractable when clinically relevant objects and imaging conditions were assumed. In this work, for the first time, estimates of the IO acting on tomographic imaging measurements were computed with consideration of realistic object variability to establish task-based performance bounds for image reconstruction methods. This was accomplished by use of a recently developed learning-based procedure. Numerical studies that were inspired by breast x-ray computed tomography were conducted to validate and demonstrate the approach. The effectiveness of the approximation method was validated on raw measurements for a signal-known-exactly and background-known-exactly (SKE/BKE) binary signal detection task.