Development of a progressive dual kriging technique for 2D and 3D multi-parametric MRI data interpolation

Abstract

In many in vivo magnetic resonance imaging (MRI) acquisitions, the image resolution is low and induces considerable segmentation errors with a poor and limited visual interpretation. Acquiring high-resolution images reduces the patient comfort and results in considerable cost because of an increase of the acquisition time. We developed a progressive technique based on multidimensional dual kriging to interpolate 2D and 3D multi-parametric MRI data. The objectives were to (1) optimise kriging parameters for 2D images and 3D volumes interpolation, (2) validate the technique in increasing the image resolution and (3) provide a direct application to 3D non-parametric volumes interpolation and image filtering. We carried out two multi-parametric MRI acquisitions on a bovine tail segment including intervertebral discs from the second to the fourth caudal vertebrae with two different spatial resolutions. We adopted the dual kriging formulation and introduced the technique of progressive kriging, which consists in kriging the given Cartesian data region-by-region. Kriging parameters were optimised to minimise the relative errors. For each MRI sequence, kriging was compared with other interpolation techniques in terms of signal mean within the region of interest, including the zero-padding, the nearest-neighbour, the bilinear and the bicubic techniques. Optimal kriging parameters for transverse relaxation time maps interpolation were a cubic covariance function and a distance of influence of only 1–8 pixels. Our technique was found to be efficient to interpolate the longitudinal and transverse relaxation times, the magnetisation transfer ratio and the apparent diffusion coefficient maps, compared with zero-padding, nearest-neighbour, bilinear and bicubic techniques. Kriging provided relatively high performance and low error, whereas image edges tend to be corrected and better defined compared with other techniques. Progressive dual kriging is a flexible technique that can be optimised to interpolate multidimensional data based on the signal distribution and should open doors to many future applications in medical imaging such as diffusion MRI, image filtering and non-parametric 3D volume reconstruction.

Keywords:

• progressive dual kriging
• magnetic resonance imaging
• relaxation times
• magnetisation transfer ratio
• diffusion tensor imaging
• interpolation
• spatial resolution
• filtering

Acknowledgements

This study was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Scoliosis Research Society (SRS).The authors would like to thank Professor Rick Hoge for the inspiring discussions and Pierre Fayant (M.Sc.A) for his support in the first steps of the development of the technique.

Competing interests: The authors declare no financial or other relationships that might create a conflict of interest.

Authors' contributions: Mohamed Aissiou carried out the developments, all the data analysis, discussed the results and drafted the manuscript. Delphine Périé proposed the design of the study, supervised all the developments, participated in the results discussion and helped to draft the manuscript. Julien Gervais participated in the design of the project, carried out the preliminary developments and supervised the further developments and data analysis. Francois Trochu supervised the kriging developments and corrected the manuscript.