[Paper Review] Sparse MRI for motion correction

Zai Yang, Cishen Zhang+1 more|arXiv (Cornell University)|Feb 1, 2013

Sparse and Compressive Sensing Techniques10 references4 citations

TL;DR

This paper proposes a sparsity-driven motion correction method for MRI that jointly estimates rigid-body translational motion and reconstructs the motion-free image using compressed sensing principles. By formulating motion as unknown parameters in the sampling system and leveraging image sparsity in the wavelet domain, the method achieves artifact reduction without requiring additional k-space data or navigator echoes, demonstrating near-perfect reconstruction on phantoms and significant artifact suppression on simulated brain data even under noise and motion.

ABSTRACT

MR image sparsity/compressibility has been widely exploited for imaging acceleration with the development of compressed sensing. A sparsity-based approach to rigid-body motion correction is presented for the first time in this paper. A motion is sought after such that the compensated MR image is maximally sparse/compressible among the infinite candidates. Iterative algorithms are proposed that jointly estimate the motion and the image content. The proposed method has a lot of merits, such as no need of additional data and loose requirement for the sampling sequence. Promising results are presented to demonstrate its performance.

Motivation & Objective

• Address the ill-posed nature of motion-corrupted MRI reconstruction by exploiting image sparsity as a prior.
• Overcome limitations of existing navigator-based methods that require extra k-space data or specific sampling sequences.
• Develop a motion correction framework that operates directly on fully sampled k-space data without additional acquisition.
• Enable motion correction in the presence of small to moderate translational motion while maintaining high image fidelity.
• Demonstrate the feasibility of joint motion and image estimation using iterative sparse reconstruction algorithms.

Proposed method

• Formulates the motion-corrupted k-space data as a phase-shifted version of the motion-free data using a translational operator Tβ, where M̄ = Tβℱm⁰.
• Introduces a sparsity constraint in the wavelet domain by minimizing the ℓ1-norm of the wavelet coefficients of the reconstructed image.
• Uses the relaxed averaged alternating reflections (RAAR) algorithm to solve the feasibility problem of finding a sparse image consistent with the corrupted k-space data.
• Implements an iterative algorithm that alternately projects onto the sparsity constraint set (S₁) and the Fourier domain consistency set (S₂), with a relaxation parameter θ = 0.9.
• Modifies the k-space data by taking the absolute value of the corrupted data to preserve amplitude and improve convergence toward the true motion-free data.
• Initializes the reconstruction with a standard inverse Fourier transform of the corrupted data, followed by iterative refinement using the SRAAR algorithm.

Experimental results

Research questions

• RQ1 Can image sparsity be effectively leveraged to correct for translational motion in MRI without requiring additional k-space data?
• RQ2 How can the joint estimation of motion and image content be formulated as a constrained optimization problem under sparsity constraints?
• RQ3 To what extent can a sparsity-driven approach outperform traditional navigator-based methods in motion correction when no extra data is acquired?
• RQ4 How does the proposed method perform under realistic conditions such as noise and varying motion amplitudes?
• RQ5 Can iterative projection algorithms like RAAR be adapted to simultaneously estimate motion and reconstruct high-quality MRI images?

Key findings

• The proposed SRAAR algorithm achieves near-perfect reconstruction of a Shepp-Logan phantom with minimal artifacts after 100 iterations, demonstrating high accuracy under ideal conditions.
• For simulated human brain data with small translational motions (within 5 pixels), the method effectively suppresses motion artifacts, even in the presence of noise, with only residual artifacts remaining.
• The method shows robustness to noise and moderate motion, but performance degrades under large motion amplitudes (three times larger than in earlier cases), indicating limitations in extreme motion scenarios.
• Each iteration of the SRAAR algorithm takes approximately 1 second on a 3 GHz CPU, enabling reconstruction of a 256×256 image in a few minutes, indicating computational feasibility.
• The algorithm can be accelerated by parallelizing motion estimation across readout lines during the projection onto the Fourier consistency set.
• The method does not require navigator echoes or oversampling, offering a significant advantage over traditional motion correction techniques in terms of scan efficiency and hardware requirements.