Isotropic Reconstruction of MR Images Using 3D Patch-Based Self-Similarity Learning

Abstract

Isotropic three-dimensional (3D) acquisition is a challenging task in magnetic resonance imaging (MRI). Particularly in cardiac MRI, due to hardware and time limitations, current 3D acquisitions are limited by low-resolution, especially in the through-plane direction, leading to poor image quality in that dimension. To overcome this problem, super-resolution (SR) techniques have been proposed to reconstruct a single isotropic 3D volume from multiple anisotropic acquisitions. Previously, local regularization techniques such as total variation have been applied to limit noise amplification while preserving sharp edges and small features in the images. In this paper, inspired by the recent progress in patch-based reconstruction, we propose a novel isotropic 3D reconstruction scheme that integrates non-local and self-similarity information from 3D patch neighborhoods. By grouping 3D patches with similar structures, we enforce the natural sparsity of MR images, which can be expressed by a low-rank structure, leading to robust image reconstruction with high signal-to-noise ratio efficiency. An Augmented Lagrangian formulation of the problem is proposed to efficiently decompose the optimization into a low-rank volume denoising and a SR reconstruction. Experimental results in simulations, brain imaging and clinical cardiac MRI, demonstrate that the proposed joint SR and self-similarity learning framework outperforms current state-of-the-art methods. The proposed reconstruction of isotropic 3D volumes may be particularly useful for cardiac applications, such as myocardial infarction scar assessment by late gadolinium enhancement MRI.

One‐millimeter isotropic breast diffusion‐weighted imaging: Evaluation of a superresolution strategy in terms of signal‐to‐noise ratio, sharpness and apparent diffusion coefficient

“…Various strategies might be envisioned to apply SR in such cases, including prospective motion management techniques (respiratory/cardiac triggering, antiperistaltic drugs) and retrospective ones (image registration and/or motion‐compensated reconstruction as in Refs. and ).…”

“…Meanwhile, Beltrami regularization provided a good compromise between noise robustness, signal fidelity and edge preservation. Other SR regularizations might be investigated to improve the results further, in particular patch‐based regularization methods . The proposed Monte Carlo simulation framework might also be used for comparing different reconstruction techniques and predicting, or at least estimating, their SNR efficiency.…”

“…This technique consists of a postprocessing step, combined with an acquisition strategy, to make high-resolution images from a set of low-resolution images of the same volume taken from different viewpoints, in different distinct fashions. [20][21][22][23][24][25][26] In anatomical MRI, a resolution enhancement can be achieved by employing the subvoxel shifted scans in the slice-selection direction or using several arbitrarily oriented scans. [20][21][22][23][24][25][26] The concept of SR has been successfully extended and applied to DWI.…”

High‐dimensionality undersampled patch‐based reconstruction (HD‐PROST) for accelerated multi‐contrast MRI

“…The patch selection operator forms a 3D tensor from a patch centered at pixel p from a set of multi‐contrast images (see optimization 2 below). Now considering the constraint , and the encoding operator , we can form the unconstrained Lagrangian of Equation 2 by linearly combining the constraint and cost functionwhere is the Lagrange multiplier, and is the penalty parameter. Equation 3 can be efficiently solved through operator‐splitting via alternating direction method of multipliers (ADMM) .…”

“…Motivated by the LLR techniques that exploit localized correlations in the contrast dimension, patch‐based image reconstructions exploiting non‐local spatial redundancies and low‐rank matrix structures have been introduced for single‐contrast MRI reconstruction to lead to even sparser representation . By modeling the similarity of image patches through block‐matching, low‐rank representation and filtering, 2D, and 3D patch‐based reconstructions have been shown to outperform conventional CS reconstructions by recovering better image details and edges and exhibiting better overall image quality.…”