Impact of denoising on precision and accuracy of saturation‐recovery‐based myocardial T₁ mapping

Abstract

3 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2017;46:1377-1388.

3D SASHA myocardial T1 mapping with high accuracy and improved precision

“…The Beltrami regularization for image denoising and enhancement was introduced for 2D natural images by Sochen et al [12] and was proposed for 2D MRI myocardial T1 mapping denoising by Bustin et al [8]. The potential of the Beltrami regularization framework lies in the general definition of the space-feature manifold and the choice of its metric.…”

“…This approach thus exploits the 3D spatial gradients of each T1-weighted image and the common edge information between T1-weighted images with varying contrast. A coupling between the T1-weighted images is performed as described by Bustin et al [8], to enforce common edge information across the 3D images in the T1 encoding direction. With this approach, common structures/edges in different T1-weighted images are preserved, while local intensity variations specific to each T1-weighted image are treated as noise, and thus reduced.…”

“…Following the derivation in Bustin et al [8], the 3D Beltrami denoising framework for 3D T1 mapping can be expressed as the following optimization problem:where are the denoised 3D T1-weighted images for the contrasts , are the corresponding 3D T1-weighted images before denoising, is the regularization parameter that controls the trade-off between the fidelity to the original acquired data and the Beltrami regularization term, is the Beltrami constant that allows selection of any arbitrary interpolation between quadratic or total variation gradient penalties, and are the 3D weighted-gradient transformation applied to the 3D T1-weighted images with varying contrast. The weighted-gradient functions penalize the gradients depending on their local orientation in order to reduce local smoothing in the directions where sharp transitions are observed, with updated at each iteration of the optimization and as a smoothing parameter.…”

“…To address this issue, efficient 2D denoising techniques have recently been proposed to reduce noise in the native T1-weighted images while preserving the inherent cardiac structures [8, 9]. Jang et al [9] employed 2D denoising based on a tissue similarity distance to reduce the sensitivity to noise of 2D STONE [10] T1 mapping when three-parameter fitting is employed.…”

“…Jang et al [9] employed 2D denoising based on a tissue similarity distance to reduce the sensitivity to noise of 2D STONE [10] T1 mapping when three-parameter fitting is employed. Bustin et al [8] developed a 2D denoising method using the Beltrami regularization to improve the precision of 2D breath-hold saturation-based myocardial T1 mapping sequences while maintaining accuracy of T1 quantification. This feature-preserving regularization technique can greatly reduce the staircase effect [11] often associated with other regularity priors.…”