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OEDIPUS: An Experiment Design Framework for Sparsity-Constrained MRI.

ABSTRACT: This paper introduces a new estimation-theoretic framework for experiment design in the context of MR image reconstruction under sparsity constraints. The new framework is called OEDIPUS (Oracle-based Experiment Design for Imaging Parsimoniously Under Sparsity constraints) and is based on combining the constrained Cramér-Rao bound with classical experiment design techniques. Compared to popular random sampling approaches, OEDIPUS is fully deterministic and automatically tailors the sampling pattern to the specific imaging context of interest (i.e., accounting for coil geometry, anatomy, image contrast, etc.). OEDIPUS-based experiment designs are evaluated using retrospectively subsampled in vivo MRI data in several different contexts. The results demonstrate that OEDIPUS-based experiment designs have some desirable characteristics relative to conventional MRI sampling approaches.

SUBMITTER: Haldar JP

PROVIDER: S-EPMC6669033 | biostudies-literature | 2019 Jul

REPOSITORIES: biostudies-literature

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OEDIPUS: An Experiment Design Framework for Sparsity-Constrained MRI.

Haldar Justin P JP Kim Daeun D

IEEE transactions on medical imaging 20190201 7

This paper introduces a new estimation-theoretic framework for experiment design in the context of MR image reconstruction under sparsity constraints. The new framework is called OEDIPUS (Oracle-based Experiment Design for Imaging Parsimoniously Under Sparsity constraints) and is based on combining the constrained Cramér-Rao bound with classical experiment design techniques. Compared to popular random sampling approaches, OEDIPUS is fully deterministic and automatically tailors the sampling patt ...[more]

PMID: 30716031

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Project description:The challenge of quantifying uncertainty propagation in real-world systems is rooted in the high-dimensionality of the stochastic input and the frequent lack of explicit knowledge of its probability distribution. Traditional approaches show limitations for such problems, especially when the size of the training data is limited. To address these difficulties, we have developed a general framework of constructing surrogate models on spaces of stochastic input with arbitrary probability measure irrespective of the mutual dependencies between individual components of the random inputs and the analytical form. The present Data-driven Sparsity-enhancing Rotation for Arbitrary Randomness (DSRAR) framework includes a data-driven construction of multivariate polynomial basis for arbitrary mutually dependent probability measures and a sparsity enhancement rotation procedure. This sparsity-enhancing rotation method was initially proposed in our previous work [1] for Gaussian density distributions, which may not be feasible for non-Gaussian distributions due to the loss of orthogonality after the rotation. To remedy such difficulties, we developed a new data-driven approach to construct orthonormal polynomials for arbitrary mutually dependent randomness, ensuring the constructed basis maintains the orthogonality/near-orthogonality with respect to the density of the rotated random vector, where directly applying the regular polynomial chaos including arbitrary polynomial chaos (aPC) [2] shows limitations due to the assumption of the mutual independence between the components of the random inputs. The developed DSRAR framework leads to accurate recovery, with only limited training data, of a sparse representation of the target functions. The effectiveness of our method is demonstrated in challenging problems such as partial differential equations and realistic molecular systems within high-dimensional (O(10)) conformational spaces where the underlying density is implicitly represented by a large collection of sample data, as well as systems with explicitly given non-Gaussian probabilistic measures.

Dataset Information

OEDIPUS: An Experiment Design Framework for Sparsity-Constrained MRI.

Publications

OEDIPUS: An Experiment Design Framework for Sparsity-Constrained MRI.

Similar Datasets

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