Fourier methods used in 2- and 3-dimensional image reconstruction can be used also in reconstructability analysis (RA). These methods maximize a variance-type measure instead of information-theoretic uncertainty, but the two measures are roughly colinear and the Fourier approach yields results close to those of standard RA. The Fourier method, however, does not require iterative calculations for models with loops. Moreover the error in Fourier RA models can be assessed without actually generating the full probability distributions of the models; calculations scale with the size of the data rather than the state space. State-based modeling using the Fourier approach is also readily implemented. Fourier methods may thus enhance the power of RA for data analysis and data mining.