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Analysis of detective quantum efficiency (DQE) is an important component of the investigation of imaging performance for flat-panel detectors (FPDs). Conventional descriptions of DQE are limited, however, in that they take no account of anatomical noise (i.e., image fluctuations caused by overlying anatomy), even though such noise can be the most significant limitation to detectability, often outweighing quantum or electronic noise. We incorporate anatomical noise in experimental and theoretical descriptions of the "generalized DQE" by including a spatial-frequency-dependent noise-power term, S(B), corresponding to background anatomical fluctuations. Cascaded systems analysis (CSA) of the generalized DQE reveals tradeoffs between anatomical noise and the factors that govern quantum noise. We extend such analysis to dual-energy (DE) imaging, in which the overlying anatomical structure is selectively removed in image reconstructions by combining projections acquired at low and high kVp. The effectiveness of DE imaging in removing anatomical noise is quantified by measurement of S(B) in an anthropomorphic phantom. Combining the generalized DQE with an idealized task function to yield the detectability index, we show that anatomical noise dramatically influences task-based performance, system design, and optimization. For the case of radiography, the analysis resolves a fundamental and illustrative quandary: The effect of kVp on imaging performance, which is poorly described by conventional DQE analysis but is clarified by consideration of the generalized DQE. For the case of DE imaging, extension of a generalized CSA methodology reveals a potentially powerful guide to system optimization through the optimal selection of the tissue cancellation parameter. Generalized task-based analysis for DE imaging shows an improvement in the detectability index by more than a factor of 2 compared to conventional radiography for idealized detection tasks.