The interferogram acquired by imaging Fourier transform spectrometer (IFTS) can’t be used directly and must be recovered. The spectrum recovery processes based on fast Fourier transform (FFT) is the traditional method which is used widely. For some IFTS, the nonuniform sampling of the interferogram is often occurrs. When the aliasing is neglected, the spectrum recovered by traditional method is often distorted. When the spectrum recovery processes based on Fourier transform are used, the precision of the recovered spectrum can be ensured, but the real-time processing requirement can’t be satisfied. In order to acquire the precise recovered spectrum of the nonuniform sampled interferogram, the interpolation method and nonuniform fast Fourier transform (NUFFT) method were adopted. For the oversampled interferogram and partial undersampled interferogram, the spectrum recovery methods based on interpolation and NUFFT were presented respectively, and the applicability of these two methods is given. Finally, the computer simulation was performed, and the results indicate that NUFFT method is preferable to interpolation method not for undersampled interferogram but for oversampled interferogram.