A diffractive plenoptic camera is a novel approach to the traditional plenoptic camera which replaces the main optic with a Fresnel zone plate making the camera sensitive to wavelength instead of range. However, algorithms are necessary to reconstruct the image produced by plenoptic cameras. While many algorithms exist for traditional plenoptic cameras, their ability to create spectral images in a diffractive plenoptic camera is unknown. This paper evaluates digital refocusing, super resolution, and 3D deconvolution through a Richardson-Lucy algorithm as well as a new Gaussian smoothing algorithm. All of the algorithms worked well near the Fresnel zone plate design wavelength, but Gaussian smoothing provided better looking images at a cost of high computation time. For wavelengths off the design wavelength, 3D deconvolution produced the best images but also required more computation time. 3D deconvolution also had the best spectral resolution, which increased away from the design wavelength. These results, along with consideration of mission constraints and spectral content in the scene, can guide algorithm selection for future sensor designs