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

Abstract

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.

Enhancing the acquisition efficiency of fast magnetic resonance imaging via broadband encoding of signal content

“…Non-Fourier encoding of the MR signal has been previously described [11,32,33], analyzed [34,35], compared to Fourier data-selective methods [29] and used for novel imaging applications [22,23]. At present, it has few, if any, routine clinical uses.…”

An efficient region of interest acquisition method for dynamic magnetic resonance imaging

“…Second, an assumption underlying both this work and the SVD method of [15] is that tailoring the excitation and reconstruction vectors using the known, previously acquired image will be useful for the subsequent problem of tracking dynamic changes. For the SVD method, this has been shown to hold for some important applications in [2] and [17]. The application of these methods to an arbitrarily specified ROI is an area in which we are currently working.…”

“…The error at a given approximation is therefore the sum of the discarded singular values, or equivalently For the approximation to be less than a given error threshold , one need only choose such that . Returning now to choose an optimal and , one may use the SVD decomposition to find and (17) APPENDIX II PROOF OF THEOREM 2 Theorem 2: For a given selection matrix , an order solution of the form or (18) will give zero error if for each column of such that . Here is the identity matrix, and is an sub-matrix of free parameters.…”

Reducing Uncertainty in Undersampled MRI Reconstruction With Active Acquisition

“…Active acquisition. Previous research on optimizing k-space measurement trajectories from the MRI community include CS-based techniques [37,33,47,9], SVD basis techniques [51,30,52], and region-of-interest techniques [44]. It is important to note that all these approaches work with fixed trajectories at inference time.…”