SparseSENSE[1] is a straightforward way to combine parallel MR imaging (pMRI) and compressed sensing (CS)[2,3] by directly replacing Fourier encoding in SparseMRI[4] with sensitivity encoding[5], and enforcing the sparsity constraint on the desired image. Self-feeding sparse SENSE (SFSS)[6] aims to address two issues of speed and robustness in sparsity-constrained pMRI, by decomposing the original SparseSENSE problem into two sub-problems: sparsity-promoting denoising problem and Tikhonov regularization problem. However, sparsity-promoting regularization term suppresses not only artifacts and noise but also some fine structures (called “feature” thereafter for short). In this paper, we add a step of feature refinement into the SFSS framework to improve the feature quality of the reconstructed image. Specifically, this step picks up the features lost from the denosing step and sends a feature-refined image to the Tikhonov regularization step as the reference.

The reconstruction problem of SparseSENSE can be formulated as$$$\min_I\sum_{j=1}^N‖F_P (S_j I)-k_j ‖_2^2 +λ‖I‖_{TV}$$$ with the total variation (TV) as one example of sparsity-promoting regularizer. To solve this problem, an auxiliary variable u is introduced and the alternating minimization strategy is used. Then, the original problem is decomposed to a TV-based sparsity-promoting denoising problem in Eq. (1.a) and a Tikhonov regularization problem in Eq. (1.b). The framework of IFR-SENSE is illustrated in Eq.(2). We used conjugate gradient (CGSENSE) to reconstruct the initial image from the partial k-space data. After TV-based denoising, we got the noise-reduced image u. As pointed in [7], the sparsity-promoting term not only suppresses the noise-like signal but also some fine small features, i.e. details in denoising. In other words, the discarded image $$$v=I-u$$$ contains not only noise-like artifacts but useful features. To address this problem, we propose to use a feature descriptor T to extract the useful features from v as $$$T\otimes v$$$ and get the feature refined image $$$I_{t}=u+T\otimes v$$$. I_t in Eq.(2.b) was then projected back into k-space using initial sensitivity maps. The fully acquired central k-space data can be inserted back to update the reconstructed k-space. And the sensitivity maps were recalculated from updated k-space data set. To improve spatial resolution of I_t, all acquired data were also inserted back to produce an improved I_t using sensitivity map-weighted summation[8]. The updated sensitivity maps and updated I_t can be used as inputs in Eq. (2.c). We got the reconstruction I after Tikhonov regularization and made it the input of TV-based denoising while the stop criterion was not met. The flowchart shown in Fig.1 summarizes the framework of IFR-SENSE described above. The feature descriptor T plays a vital role in this framework. It is calculated by $$$T=1-|c(p,q)s(p,q)|=1-|\frac{2σ_{pq}+C1}{σ_p^2+σ_q^2+C1}|$$$, where p and q denote two local image patches extracted from the magnitude part of u and its corresponding deblurred image obtained by the convolution with a Gaussian kernel. c(p,q) denotes the contrast variation and s(p,q) denotes the structure correlation. Please refer to [9] for details. The value of each element in the feature descriptor image is in the interval [0,1]. The more its value is close to 1, the higher probability it belongs to the structure part.

$$\begin{cases}u^k=argmin_u‖I^k -u^k ‖_2^2+λ_{TV} ‖u^k ‖_{TV} &(1.a)\\I^{k+1}=argmin_I∑_{j=1}^N‖F_P (S_j I^{k+1} )-k_j ‖_2^2 +μ‖I^{k+1} -u^k ‖_2^2 & (1.b)\end{cases}$$

$$\begin{cases}u^k=argmin_u‖I^k -u^k ‖_2^2+λ_{TV} ‖u^k ‖_{TV} &(2.a)\\I_t^k=u^k+T^k⊗(I^k -u^k) & (2.b)\\I^{k+1}=argmin_I∑_{j=1}^N‖F_P (S_j I^{k+1} )-k_j ‖_2^2 +μ‖I^{k+1} -u^k ‖_2^2 & (2.c)\end{cases}$$

The raw measurement data were obtained from a GE scanner (GE Healthcare, Waukesha, WI) with 32-element head coils and 3D T1-weighted spoiled gradient echo sequence, TE=minimum full, TR=7.5ms, FOV=24×24cm, matrix=256×256 and slice thickness=1.7mm. The full k-space data were acquired and manually down-sampled to simulate a reduction factor of 6 using a Possion-disc sampling trajectory. The 32 central k-space lines were used for estimating the initial channel sensitivity profiles. The sum-of-square reconstruction from full data is used as the reference. Fig.2 shows the comparison of the proposed method with self-feeding sparse SENSE (SFSS). In addition, the corresponding region defined by the red box in Fig2.(a) was zoomed to reveal details. It can be seen that IFR-SENSE restores the image details more accurately than SFSS.We propose a simple and effective way to refine the useful features in self-feeding sparse SENSE framework. The results demonstrate the superior performance of the proposed method in terms of detail preservation.