Hyperspectral sensors observe hundreds or thousands of narrow contiguous spectral bands. The use of hyperspectral imagery for remote sensing applications is new and promising, yet the characterization and analysis of such data by exploiting both spectral and spatial information have not been extensively investigated thus far. A generic methodology is presented for detecting and compensating anomalies from hyperspectral imagery, taking advantage of all information available -- spectral and spatial correlation and any a priori knowledge about the anomalies. An anomaly is generally defined as an undesired spatial and spectral feature statistically different from its surrounding background. Principal component analysis (PCA) and the Iterative Order and Noise (ION) estimation algorithm provide valuable tools to characterize signals and reduce noise. Various methodologies are also addressed to cope with nonlinearities in the system without much computational burden. An anomaly compensation technique is applied to specific problems that exhibit different stochastic models for an anomaly and its performance is evaluated.