We explore the use of the Pixon method, one of the highest performance image reconstruction methods available today, for the analysis of electron energy loss spectra (EELS). The method takes particular advantage of two-dimensional (2-D) CCD data, in which the data are blurred by a PRF (point-response-function as measured by the low-loss spectrum) both in the direction of energy dispersion and in the cross-dispersion direction. The Pixon method is used to simultaneously (i) deconvolve the PRF, increasing the spectral resolution, and (ii) fit the data in the cross-dispersion direction which efficiently combines the signal into a single parent spectrum. Relative to 1-D methods, we demonstrate that our 2-D treatment (i) more effectively detects weak features and (ii) allows EELS methods to be applied to much lower signal-to-noise ratio data. Both of these advantages are critical to the future development of EELS analysis.