Superresolution in MRI—perhaps sometimes

Soon after publication of the aforementioned Communication and upon deeper examination of the subject, we began to be puzzled as to the origin of the apparent resolution improvement. Fourier-encoded MRI data is inherently band-limited, which would prevent the theoretical possibility of superresolution enhancement without the incorporation of prior knowledge. But the result of the superresolution procedure does seem, by means of visual inspection, sharper than the zero-padded result of an equivalent number of averages. Also, the power of the spatial frequency spectrum (k-space) of the superresolution result is decidedly non-zero far beyond the original borders defined by the low resolution images. We agree, of course, that pure postprocessing cannot add information and that shifting of optimally sampled data in the presence of white noise does nothing. But field-of-view shifts, at least in the case of one manufacturer of MRI systems, are orchestrated by modulations of both the receiver phase and the receiver frequency in the case of shifts in the read-out direction, and by modulations of the receiver phase for spatial shifts in the phase-encode direction. These modulations may be considered part of the measurement procedure and as such are not postprocessing steps. In addition, the MR signal acquisition process involves various filtering steps which can include the decimation of oversampled data, while image reconstruction procedures often involve the interpolation of k-space values (e.g., ramp sampling), and low-pass filtering of k-space to reduce noise (e.g., a fermi filter). The superresolution algorithm might be restoring previously attenuated frequencies, or, in the worst case, adding frequencies artifactually. In summary, although we witnessed some apparent improvement in the level of detail visible in MR images after applying a superresolution algorithm to shifted images, superresolution probably only has a future in MRI in cases where non-Fourier encoding is used (e.g., wavelet encoding). A recently accepted paper of ours deals with a possible resolution improvement in the case of radio-frequency encoding, and addresses the limitations of superresolution as applied to Fourier encoding.