Proton MR spectroscopic imaging (MRSI) of human cerebral cortex is complicated by the presence of an intense signal from subcutaneous lipids, which, if not suppressed before Fourier reconstruction, causes ringing and signal contamination throughout the metabolite images as a result of limited k‐space sampling. In this article, an improved reconstruction of the lipid region is obtained using the Papoulis‐Gerchberg algorithm. This procedure makes use of the narrow‐band‐limited nature of the subcutaneous lipid signal to extrapolate to higher k‐space values without alteration of the metabolite signal region. Using computer simulations and in vivo experimental studies, the implementation and performance of this algorithm were examined. This method was found to permit MRSI brain spectra to be obtained without applying any lipid suppression during data acquisition, at echo times of 50 ms and longer. When applied together with optimized acquisition methods, this provides an effective procedure for imaging metabolite distributions in cerebral cortical surface regions.