Prior ensemble learning: Theory and application to MR image priors

Nanako Kubota, Yufu Kasahara, Ken Harada, Koji Fujimoto, Tomohisa Okada, Masato Inoue*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Purpose: Compressed sensing (CS) reduces the measurement time of magnetic resonance (MR) imaging, where the use of regularizers or image priors are key techniques to boost reconstruction precision. The optimal prior generally depends on the subject and the hand-building of priors is hard. A methodology of combining priors to create a better one would be useful for various forms of image processing that use image priors. Methods: We propose a theory, called prior ensemble learning (PEL), which combines many weak priors (not limited to images) efficiently and approximates the posterior mean (PM) estimate, which is Bayes optimal for minimizing the mean squared error (MSE). The way of combining priors is changed from that of an exponential family to a mixture family. We applied PEL to an undersampled (10%) multicoil MR image reconstruction task. Results: We demonstrated that PEL could combine 136 image priors (norm-based priors such as total variation (TV) and wavelets with various regularization coefficient (RC) values) from only two training samples and that it was superior to the CS-SENSE-based method in terms of the MSE of the reconstructed image. The resulting combining weights were sparse (18% of the weak priors remained), as expected. Conclusion: By the theory, the PM estimator was decomposed into the sparse weighted sum of each weak prior’s PM estimator, and the exponential computational complexity for RCs was reduced to polynomial order w.r.t. the number of weak priors. PEL is feasible and effective for a practical MR image reconstruction task.

Original languageEnglish
Pages (from-to)1937-1945
Number of pages9
JournalInternational Journal of Computer Assisted Radiology and Surgery
Issue number11
Publication statusPublished - 2021 Nov


  • Compressed sensing
  • Image prior distribution
  • Machine learning
  • Parallel MR imaging

ASJC Scopus subject areas

  • Surgery
  • Biomedical Engineering
  • Radiology Nuclear Medicine and imaging
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Health Informatics
  • Computer Graphics and Computer-Aided Design


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