High spatiotemporal resolution 3D imaging is a desired technique for detecting dynamic information of detailed anatomy and getting accurate modeling parameters. However, low efficiency of MR signal acquisition and motion artifacts are always challenging in dynamic MRI. Recently radial sampling is widely used because of its high motion insensitivity. Additionally, a complement reconstruction method called GRASP ^[1] was developed for high spatiotemporal 3D dynamic imaging. As a matter of fact, we once proposed a method using golden angle spiral for 3D dynamic imaging ^[2], in which compressed sensing (CS) with L1 minimization was used and the spatiotemporal resolution was improved greatly. We call this method spiral sparse parallel imaging (SpiralSP-L1). To improve the temporal resolution and accuracy further, CS with L0 minimization is investigated ^[3] for the spiral data reconstruction (SpiralSP-L0) in this abstract, which provides high image quality as well as high temporal precision.

Simulations were performed on a numerical phantom (Fig. 1). In the phantom, a large disc moved from the right side to the left; and the contrast in a small disc was changing during the movement. There is also a small bright point in the phantom which represents a detailed structure.

In-vivo experiments were performed on a GE 3T MR750 scanner (GE Healthcare, Waukesha, WI) with an 8 channel coil. A 3D stack of golden angle spiral was used to acquire k-space data. The scan parameters were TR/TE=5.9ms/0.3ms, FOV=360×360×160mm³, in-plane resolution=1.41×1.41mm², slice thickness=5mm, interleave number for each slice=192, total scan time=30sec. The subject was required to breathe shallowly when scanning. Compressed sensing with homotopic L0 minimization ^[3] was used in the reconstruction. The sparse domain was temporal total variation (TV) domain. The reconstruction equation was shown as follows: $$\min\left\{\parallel F\cdot S\cdot d\parallel_2^2+\lambda\cdot \lim_{\sigma \rightarrow 0}\sum_{n\in\Omega}(1-e^{-\frac{|u(n)|}{\sigma}})\right\}, u=T\cdot d$$In this equation, the first part is a SENSE item which guarantees the data consistency ($$$d$$$ is the image series, $$$S$$$ is the sensitivity map, $$$F$$$ is the non-Cartesian Fourier transform, $$$m$$$ is the acquired data), and the second part is an approximation of L0 norm ($$$T$$$ is a temporal TV operator and $$$\lambda$$$ is a regularization parameter).

The fully sampled k-space data for 1 frame (including simulation and in-vivo data) consisted of 48 interleaves. We used 2 interleaves to reconstruct 1 frame, corresponding to an acceleration factor of 24. With such a high undersampling rate, the 3D temporal resolution for in-vivo data was about 312ms.

Three reconstruction algorithms were compared with each other including Temporal Resolution Acceleration with Constrained Evolution Reconstruction (TRACER) ^[4], SpiralSP-L1 and SpiralSP-L0. Two representative frames were selected to evaluate the algorithms. Fig. 2 shows the simulation results. The result of SpiralSP-L0 shows least motion artifacts and highest SNR. Furthermore, the detailed structure (red arrow) can be preserved best. Fig. 3 shows intensity curves from the small disc region, in which we can see that the result of TRACER is too noisy and SpiralSP-L1 has some smoothing effects. The result of SpiralSP-L0 has the best temporal accuracy. The relationship between the temporal resolution and temporal accuracy is shown in Fig. 4, which indicates that, for all algorithms, the higher reconstructed temporal resolution is the more accurate the intensity curve is. For the shallow breathing in-vivo data in Fig. 5, the results from SpiralSP-L0 also show the best image quality with least artifacts and highest SNR.The CS theory is based on L0 norm minimization theoretically; however solving this problem numerically is not straightforward. So L1 norm is commonly used in the CS reconstruction. When the undersampling rate becomes higher, L1 norm cannot recover images well any more. In comparison, in this study, L0 norm CS shows better reconstructed images than L1 norm. For TRACER, it exploits the strong relationship between two consecutive frames. So TRACER is vulnerable to motion and resultant images may show large intensity fluctuations. Because CS exploits the relationship of all frames, it is immune to intensity fluctuations. For detailed structures and temporal accuracy, sufficient spatiotemporal resolution is desired, which requires a high undersampling rate. Considering the acquisition efficiency and motion insensitivity of spiral, SpiralSP-L0 may be a potential solution.A new dynamic 3D imaging method is investigated which combines golden angle spiral trajectories and the reconstruction algorithm of CS with L0 minimization. This technique is highly motion insensitive and acquisition efficient so that it is very promising to achieve high spatiotemporal resolution imaging in clinical applications.