Interferometric hyperspectral imaging can obtain the spatial information and spectral characteristics of the target. It plays an important role in many fields such as biomedicine，material analysis，food safety and cultural relic archaeology. The interferometric hyperspectral imaging based on symmetric wedgy cavity provides a new method for spectral detection. By analyzing the interference principle and working mode，the spectrum recovery method is studied. In order to eliminate the effect of image-plane macula on spectrum recovery，an interferogram correction algorithm is proposed. A fast subpixel image registration algorithm based on local phase correlation can realize accurate extraction of the interference data in holistic push-broom mode. A spectrum recovery method based on matrix inversion is presented by discussing the systemic spectral transfer matrix. A prototype is developed for a spectral imaging experiment and the preliminary recovered results are obtained with the proposed spectrum recovery method.