Nonlinear Interpolation in the Fourier Domain Guided by Morphologic Filters

Preeti Gopal, David Bailey, Imants Svalbe

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

1 Citation (Scopus)


Morphologic filters are used here to interpolate missing values from sets of frequency domain measurements, as occurs in Magnetic Resonance Imaging. MRI data acquisition is done in the Fourier domain which is often sub-sampled to reduce the required scan time. Partial recovery of the missing frequency samples permits direct Fourier inversion to provide a rapid and improved initial estimation of the spatial data. The interpolated image should also improve the convergence of subsequent iterative reconstruction that is used in compressed sensing methods. Spectral analysis of morphologic operators appears rarely in prior publications. We examine the non-linear spectral changes that arise from applying morphologic open and close operations. We use a form of alternating sequential filters (like those proposed by Jean Serra in 1988) to expand the content of the Fourier spectrum around the known measured values. The alternating sequence terminates just before the structuring element size that maximises the added spectral energy. The maximum in spectral energy coincides with the optimal reconstructed psnr. This interpolation, being idempotent, at worst, adds nothing to the known data. The method is, of course, sensitive to both the Fourier sub-sampling pattern and to the spectral content of the data. It thus works best for data that contains strong steps between flat zones rather than images comprised mostly of smooth curves. This nonlinear interpolation method can increase the mean psnr values by 3 for sampling rates above 70%. In the most favourable cases, psnr gains well above 20 can be obtained for sampling rates down to 60%, with psnr gains above 10 possible for sampling rates as low as 20%.

Original languageEnglish
Title of host publicationDICTA 2017 - 2017 International Conference on Digital Image Computing
Subtitle of host publicationTechniques and Applications
EditorsYi Guo, Hongdong Li, Weidong (Tom) Cai, Manzur Murshed, Zhiyong Wang, Junbin Gao, David Dagan Feng
Place of PublicationPiscataway NJ USA
PublisherIEEE, Institute of Electrical and Electronics Engineers
Number of pages8
ISBN (Electronic)9781538628393
Publication statusPublished - 19 Dec 2017
EventDigital Image Computing Techniques and Applications 2017
- Novotel Sydney Manly Pacific , Sydney, Australia
Duration: 29 Nov 20171 Dec 2017
Conference number: 19th (Proceedings)


ConferenceDigital Image Computing Techniques and Applications 2017
Abbreviated titleDICTA 2017
Internet address


  • alternating sequential filters
  • Fourier interpolation
  • granulometry
  • kspace sub-sampling
  • Morphologic filters

Cite this