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A variety of spaceborne remote sensing instruments achieve wide-area coverage with only a small number of detectors, by using a cross-track scanning mechanism and satellite motion to provide extended coverage. Errors in the detectors' relative calibrations result in stripes in the images acquired by these instruments. This letter presents a general approach for equalizing the detector responses, based on scene statistics. For the case where the detector response functions are predominantly linear, with a small quadratic component, a complete set of equations for implementing the statistics-based calibration is also presented. The resulting algorithm has been tested with application to a few select Earth scenes from the Moderate Resolution Imaging Spectroradiometer, and the quality of the resulting calibration functions is discussed. Based on the mathematical formulation and intuitive reasoning, recommendations are offered for selecting scenes that are suitable for determining the detectors' relative calibrations with validity across the full dynamic range of the instrument.