Covariance Map Convolution for MRI Data Estimation
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Solution Overview
Problem
Reconstructing non-Cartesian parallel imaging scans in MRI is computationally burdensome, particularly due to the need for fixed geometries and iterative processes in existing methods like GRAPPA and iterative SENSE.
Innovation Solution
The method employs covariance maps to estimate and synthesize k-space data through convolution operations, allowing for image reconstruction without requiring fixed geometries or extensive iterative processes, thereby reducing computational burden and increasing speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If iterative processes and fixed geometries are used in GRAPPA and iterative SENSE methods, then image reconstruction accuracy is improved, but computational burden and scan time increase significantly
Solution Approach 1:
The patent pre-computes and stores covariance maps during a calibration phase using fully sampled k-space data. These covariance maps are then reused during the actual imaging acquisition to enable rapid convolution operations, eliminating the need for iterative computations during scan time. This preliminary action resolves the contradiction by preparing computational resources in advance while maintaining reconstruction accuracy.
Solution Approach 2:
The patent replaces the iterative computational processes (mechanical system) with a direct convolution operation based on pre-computed covariance maps. This substitution transforms the computational approach from iterative refinement to a single-step convolution, dramatically reducing scan time while preserving image reconstruction accuracy through the mathematical equivalence of the covariance-based convolution to the iterative processes.
2Productivity
If existing parallel imaging methods are used, then imaging speed is improved, but memory requirements and computational complexity increase
Solution Approach 1:
The patent segments the computational task by separating the covariance map computation (performed once during calibration using fully sampled data) from the imaging reconstruction (performed rapidly using pre-computed covariance maps). This segmentation allows the system to achieve high imaging speed during acquisition while keeping computational complexity manageable, as the complex covariance calculation is performed only once and stored for rapid reuse.
Solution Approach 2:
The patent performs the computationally intensive covariance map calculation as a preliminary action during calibration, storing the results for rapid retrieval and convolution during actual imaging. This preliminary computation shifts the computational burden from the imaging acquisition phase to the calibration phase, enabling high imaging speed without proportionally increasing real-time computational complexity.
3Loss of time
If non-Cartesian sampling trajectories are used, then scan time is reduced, but the complexity of data synthesis and reconstruction increases
Solution Approach 1:
The patent creates a universal reconstruction framework where the same covariance-based convolution operation can handle both Cartesian and non-Cartesian sampling trajectories. The covariance maps serve as a universal tool that works regardless of the specific k-space sampling pattern, allowing the system to maintain simple data synthesis complexity while achieving reduced scan times through non-Cartesian trajectories like radial or spiral sampling.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly reduces scan time and memory requirements, making it faster and more efficient than existing methods, especially for 3D non-Cartesian imaging, by enabling data synthesis on arbitrary trajectories with minimal memory usage.
Implementation Method 1
Magnetic resonance imaging ('MRI') uses the nuclear magnetic resonance ('NMR') phenomenon to produce images. When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the nuclei in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency.
Implementation Method 2
When utilizing these 'MR' signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used.
Implementation Method 3
If the substance, or tissue, is subjected to a magnetic field (excitation field B1) that is in the x-y plane and that is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or 'tipped,' into the x-y plane to produce a net transverse magnetic moment Mxy.
Implementation Method 4
Intermediate data are estimated using the acquired data and the produced covariance maps. A desired k-space sampling pattern is selected, and synthesized data are produced on this selected k-space sampling pattern by convolving the intermediate data with the covariance maps.
Data Source
AI summary
Described here are systems and methods for reconstructing images of a subject using a magnetic resonance imaging (“MRI”) system. As part of the reconstruction, synthesized data are estimated at arbitrarily specified k-space locations from measured data at known k-space locations. In general, the synthesized data is estimated using a convolution operation that is based on measured or estimated covariances in the acquired data. The systems and methods described here can thus be referred to as Convolution Operations for Data Estimation from Covariance (“CODEC”).