Deconvolution-interpolation gridding (DING): accurate reconstruction for arbitrary k-space trajectories.

Area of Science:

• Medical Imaging
• Signal Processing
• Computational Science

Background:

• Reconstructing images from arbitrarily-sampled k-space data is a significant challenge in MRI.
• Conventional gridding methods often require grid oversampling or complex density compensation functions.
• These limitations can impact memory usage and reconstruction accuracy, especially for 3D trajectories and during patient motion.

Purpose of the Study:

• To introduce a novel iterative algorithm, deconvolution-interpolation gridding (DING), for accurate image reconstruction from non-uniformly sampled k-space data.
• To address limitations of existing gridding techniques, including memory inefficiency and difficulties with sampling density compensation.
• To provide a robust reconstruction method suitable for dynamic or unpredictable k-space trajectories.

Main Methods:

• DING solves a sparse system of linear equations equivalent to k-space deconvolution.
• The algorithm utilizes the conjugate gradient (CG) method for efficient inversion of the sparse system.
• It avoids grid oversampling and the need for a sampling density compensation function.

Main Results:

• DING demonstrated increased reconstruction accuracy without grid subsampling.
• The method showed stable performance and reduced root mean square (RMS) error across various k-space trajectories.
• Simulations and in vivo spiral MRI experiments confirmed DING's effectiveness compared to conventional methods.

Conclusions:

• The deconvolution-interpolation gridding (DING) algorithm offers an efficient and accurate solution for reconstructing MRI images from arbitrarily-sampled k-space.
• DING's ability to handle non-uniform sampling and avoid problematic components makes it valuable for advanced imaging scenarios, including those with patient motion.
• The algorithm's memory efficiency is particularly advantageous for 3D MRI reconstructions.