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Improving radial cardiac cine with higher-order total-variation regularizations1MDACC, Houston, TX, United States, 2UIHA, Houston, TX, United States, 3IUFW, Fort Wayne, IN, United States
Synopsis
In cardiac cine MRI, radial data acquisition will make the motion effects being more noise-like in image domain, and to achieve high temporal resolution, sparse sampling will inevitably lead to streaking artifacts using conventional image reconstruction methods. Golden angle radial reordering which provides continuously change in angle direction will eliminate the coherence of (streaking) artifacts in the temporal dimension. While GRASP-like reconstruction method applies 1D total-variation (TV) regularization on the reconstructed temporal signal, the spatial consistence of the reconstructed images are not ensured. Here we propose a reconstruction strategy using a higher-order TV to promote the spatial imaging quality.
Introduction
Conventional cardiac MR (CMR) cine is synthesized from data acquired over multiple heartbeats, and therefore it is sensitive to changes in the cardiac cycle duration, which occur during arrhythmias, and moreover inconsistent breath holding will cause variations in respiratory position. Those situations become even more challenging for high-resolution, dynamic, or 3D acquisitions, which requires more data acquisition. One approach towards the above challenges is based on radial acquisition scheme. The golden angle (GA) radial reordering could provide a near-uniform k-space sampling within image reconstruction time window [1] and thus allow for retrospective choice of temporal resolution [2].
The rationale behind CMR reconstruction based on radial acquisition is making the motion effects in image domain being more noise-like, while the sparse sampling (much lower number of spokes in k-space than data samples per spoke) due to increased higher temporal resolution will inevitably lead to (streaking) artifacts in conventional image reconstruction methods. One would expect that if the artifacts on a voxel behave like noise in the temporal dimension in image domain, then the filtering method would be helpful to retrieve the true dynamic information from the noise-like temporal signal. The reconstruction of artifact-free images from radially encoded MRI acquisitions poses a difficult task for undersampled data sets, towards that, we need to ensure the (streaking) artifacts will not coincidently happen in two consecutive temporal location for each voxel, and GA radial reordering could provide continuously change in angle direction to help in eliminating the coherence of (streaking) artifacts in the temporal dimension.
There are a few available methods for fulfilling the temporal filtering in CMR reconstruction. The Kalman filter is the most known method [3], and other approaches include dictionary-based method [4], and end-to-end approaches [5]. An elegant method is GRASP which applied 1D total-variation (TV) regularization on the reconstructed temporal signal [6]. Since GRASP will not ensure the spatial consistence of the reconstructed images, and radial acquisition is making the motion effects in image domain being more noise-like, we propose to apply higher-order TV on the reconstruction to improve the spatial imaging quality.
Methods
Considering the constrained optimization problem $$$\min_{x}f\left(x\right)$$$, where x belongs to the domain of definition, then it can be transformed into unconstrained optimization problem $$$\min_{x}f\left(x\right)+I\left(x\right)$$$, where I(x) is an indication function on the defined domain. Using the proximal gradient method, then $$$x_{\left(k\right)}=prox_{t\left(k\right)I}\left(x_{k}-t_{k}grad f\left(x_{k}\right) \right)$$$, $$$prox_{t\left(k\right)I}$$$ is the proximal mapping of the indicator function I(x), t(k) is the step length, since the proximal mapping of indicator function is a simple projection operator, the calculation is simplified [7]. Thus, our optimization problems minx f (x) +sum (regularizers) and minx f(x) + I(x) +sum (regularizers) are equivalent, so that we can use the proximal mapping of the indicative function in the algorithm [7]. The flexible fulfillment of convex optimization with non-smooth regularlzers is developed along the concept mentioned above and is demonstrated on various reconstruction problems in [8], which was derived from the original algorithm in [8]. Essentially, the method will find $$$x=arg min_{x}f\left(x\right)+g\left(x\right)+\sum_\left(m=1\right)^Mh_{m}\left(L_{m}x\right)$$$, where the first term can be data consistence constraints, the second term will be an indicator function which changes original domain-constrained problem into a non-constrained problem, and the multiple (M) regularizers (various order TVs on spatial/temporal-dimension contents) can be flexibly included in the third term [6] (see Fig. 1).Results
The CMR data is acquired using a radial bssfp ( FOV = 350mm*350mm*126mm, spatial resolution = 1.2mm*1.2mm*3.5mm, acquisition time ~ 90s, TE/TR = 1.75ms/3.88ms, BW = 600Hz/pixel. Temporal resolution is depending on reconstruction settings (15 spokes/frame with 25 iterations).
Figure 2 is CMR cine image frames reconstructed by no-uniform FFT of zero-filling and TVs regularization, with weighting parameters: temporal TV operator = 0.09, spatial TV operator = 0.007, and spatial second order TV operator = 0.003.
Discussion and Conclusion
Inherent spatial/temporal noise as well as spatial streaking artifacts were unified reduced by 1D temporal TV regularizer and spatial second order TV regularizer, we provide a practical approach to fulfill this duty.
Our approach is easy in implementation and the result is reliable than conventional methods. Since it’s flexible in including (non-smooth) regularizers, better results could be expected by diligently design of the regularizers. On the other hand, our method can be modified to be used in the more sophisticated scenario where higher order TVs could be applied on the reconstructed images in the TV-oriented sub-optimization such as in [4].
Acknowledgements
No acknowledgement found.References
[1] IEEE Trans Med Imaging. 2007 Jan; 26(1):68-76, [2] Magn Reson Med. 2016 Jul; 76(1):94-103, [3] Ch4, www.cambridge.org/9781107103764, [4] IEEE TMI, pp 1132-1145, vol.32(6) , [5] https://arxiv.org/abs/1503.06383, [6] Magn Reson Med. 2014; 72:707–717, [7] ISMRM 2017. 1427, [8] Laurent Condat, J Optim Theory Appl (2013) 158:460–479.Figures
