This paper presents a case study from a single, 6h observing period to illustrate the application of techniques developed for interferometric radio telescopes to the spectral analysis of observations of ionospheric fluctuations with sparse arrays. We have adapted the deconvolution methods used for making high dynamic range images of cosmic sources with radio arrays to making comparably high dynamic range maps of spectral power of wavelike ionospheric phenomena. In the example presented here, we have used observations of the total electron content (TEC) gradient derived from Very Large Array (VLA) observations of synchrotron emission from two galaxy clusters at 330MHz as well as GPS-based TEC measurements from a sparse array of 33 receivers located within New Mexico near the VLA. We show that these techniques provide a significant improvement in signal-to-noise ratio (S/N) of detected wavelike structures by correcting for both measurement inaccuracies and wavefront distortions. This is especially true for the GPS data when combining all available satellite/receiver pairs, which probe a larger physical area and likely have a wider variety of measurement errors than in the single-satellite case. In this instance, we found that the peak S/N of the detected waves was improved by more than an order of magnitude. The data products generated by the deconvolution procedure also allow for a reconstruction of the fluctuations as a two-dimensional waveform/phase screen that can be used to correct for their effects.