PurposeIn this work, the limits of image reconstruction in k-space are explored when non-bijective gradient fields are used for spatial encoding. TheoryThe image space analogy between parallel imaging and imaging with non-bijective encoding fields is partially broken in k-space. As a consequence, it is hypothesized and proven that ambiguities can only be resolved partially in k-space, and not completely as is the case in image space. MethodsImage-space and k-space based reconstruction algorithms for multi-channel radiofrequency data acquisitions are programmed and tested using numerical simulations as well as in vivo measurement data. ResultsThe hypothesis is verified based on an analysis of reconstructed images. It is found that non-bijective gradient fields have the effect that densely sampled autocalibration data, used for k-space reconstruction, provide less information than a separate scan of the receiver coil sensitivity maps, used for image space reconstruction. Consequently, in k-space only the undersampling artifact can be unfolded, whereas in image space, it is also possible to resolve aliasing that is caused by the non-bijectivity of the gradient fields. ConclusionFor standard imaging, reconstruction in image space and in k-space is nearly equivalent, whereas there is a fundamental difference with practical consequences for the selection of image reconstruction algorithms when non-bijective encoding fields are involved. Magn Reson Med 73:857-864, 2015. (c) 2014 Wiley Periodicals, Inc.