Applicability and efficiency of near-optimal spatial encoding for dynamically adaptive MRI.

Adaptive near-optimal MRI spatial encoding entails, for the acquisition of each image update in a dynamic series, the computation of encodes in the form of a linear algebra-derived orthogonal basis set determined from an image estimate. The origins of adaptive encoding relevant to MRI are reviewed. Sources of error of this approach are identified from the linear algebraic perspective where MRI data acquisition is viewed as the projection of information from the field-of-view onto the encoding basis set. The definitions of ideal and non-ideal encoding follow, with nonideal encoding characterized by the principal angles between two vector spaces. An analysis of the distribution of principal angles is introduced and applied in several example cases to quantitatively describe the suitability of a basis set derived from a specific image estimate for the spatial encoding of a given field-of-view. The robustness of adaptive near-optimal spatial encoding for dynamic MRI is favorably shown by results computed using singular value decomposition encoding that simulates specific instances of worst case data acquisition when all objects have changed or new objects have appeared in the field-of-view. The mathematical analysis and simulations presented clarify the applicability and efficiency of adaptively determined near-optimal spatial encoding throughout a range of circumstances as may typically occur during use of dynamic MRI.