Hyperspectral anomaly detection aims to fast and credibly find nontrivial candidate targets without prior knowledge, which has become an increasingly pressing need as imagery swath and resolution are growing rapidly. Relevant state-of-the-art learning-based anomaly detection approaches have benefited from data-driven hierarchical feature embeddings that typically model the geometric distribution of spectral vectors. However, most of these techniques are incompatible with resource-constrained applications: 1) huge computational costs caused by feedforward convolution operation cannot be supported with limited computation resources and storage (e.g., in-orbit processing); 2) detection accuracy relies on large-scale training datasets, which results in labor-expensive imagery collection, pixel-level labeling, and timeconsuming learning procedure. To address these issues, we advocate a learning-free, frequency domain anomaly detection method combined with predictive coding, an intriguing heuristic prior from human vision system. Technically, 1) inherently efficient frequency transformation could be implemented with existing image compression modules (e.g., JPEG or JPEG2000 codec), which improves the utilization of computational resources; 2) predictive coding mechanism is exploited for suppressing frequently occurring information represented in the low-entropy frequency domain, such that the "unpredictive" subject (i.e., anomaly spectrums) can "pop out" with naive residuals. Such heuristic prior incorporated into the computational model can reduce dependence on the large-scale training set. Experiments on real-world hyperspectral datasets confirm the efficacy of our model. Besides, low computation cost of the proposed (fast frequency transformation and analytical solutions) anomaly detector facilitates rather straightforward sliding window verification in high-resolution imagery.