Non-quadratic convex regularized reconstruction of MR images from spiral acquisitions

TL;DR

This paper introduces a novel non-quadratic convex regularization method for reconstructing MR images from spiral and non-Cartesian acquisitions, improving image quality by directly modeling data without interpolation artifacts.

Contribution

It proposes a general reconstruction framework that directly incorporates exact k-space data locations and object characteristics using a non-quadratic convex optimization, enhancing image quality.

Findings

Improved image reconstruction quality on simulated data.

Effective application to real spiral MR acquisitions.

Enhanced signal-to-noise ratio and spatial resolution.

Abstract

Combining fast MR acquisition sequences and high resolution imaging is a major issue in dynamic imaging. Reducing the acquisition time can be achieved by using non-Cartesian and sparse acquisitions. The reconstruction of MR images from these measurements is generally carried out using gridding that interpolates the missing data to obtain a dense Cartesian k-space filling. The MR image is then reconstructed using a conventional Fast Fourier Transform. The estimation of the missing data unavoidably introduces artifacts in the image that remain difficult to quantify. A general reconstruction method is proposed to take into account these limitations. It can be applied to any sampling trajectory in k-space, Cartesian or not, and specifically takes into account the exact location of the measured data, without making any interpolation of the missing data in k-space. Information about the expected characteristics of the imaged object is introduced to preserve the spatial resolution and improve the signal to noise ratio in a regularization framework. The reconstructed image is obtained by minimizing a non-quadratic convex objective function. An original rewriting of this criterion is shown to strongly improve the reconstruction efficiency. Results on simulated data and on a real spiral acquisition are presented and discussed.