Transform coefficients carry important data characteristics but can also be compressed significantly in many remote sensing applications. Failures in the several computing facilities that execute lossy compression algorithms and support the transmission of Fourier transform data can corrupt the values beyond recovery at the final destination. Various methods for including fault tolerance at the data processing level are exemplified by describing a protected system that computes the FFT, truncates small coefficients and compresses the remaining nonzero coefficients using lossless arithmetic coding. Algorithmic checks within the FFT and arithmetic encoding and decoding operations are augmented with additional features between and across several subsystems involved in compressing and transmitting the FFT data. End-to-end error detection is achieved in this manner.