Figure 1.
Diagram of the proposed interpolated Compressed Sensing (iCS) method.
It contains total 3 steps: Step1, calculating the weighting function which maps the raw data from the neighboring slice (Slice2) to the target slice (Slice1) by acquiring low resolution full k-space images of the two adjacent slices; Step2, estimating the missed k-space data of the target slice (Slice1) by using the raw data of its neighboring slice (Slice2) convolved by the weighting function; Step3, k-space data interpolation and image reconstruction of the target slice (Slice1).
Figure 2.
Multi-slice two dimensional sparse MR imaging strategy used in the MR experiment.
Total 9 slices were obtained and were grouped into 3 groups. In each group the slice at the middle was undersampled at low undersampling rate of 1/4, while the other two slices were undersampled at rate of 1/100. The middle slice was thus used to estimate the missed k-space data of the two neighboring slices. That is, the slices of #2, #5 and #8 were undersampled at 1/4 rate and used to interpolate the missing k-space data of the slices of #1 and #3, #4 and #6, #7 and # 9, respectively.
Figure 3.
In-vivo MR images of human feet in sagittal plane.
Each slice (i.e., slice #1, #3, #4, #6, #7, and #9) was reconstructed using the three methods: conventional full k-space reconstruction (which served as the reference in the 1st column), conventional Compressed Sensing at undersampling rate of 1/100 (in the 2nd column), conventional Compressed Sensing at undersampling rate of 1/11 (in the 3rd column), and the proposed interpolated CS methods at the undersampling rate 1/100 (in the 4th column). In this comparison study, image quality improvement of the iCS reconstruction method is observed compared with the CS method, much image details being recovered.
Figure 4.
The Contrast to Noise Ratio (CNR) maps of the full k-space reference images, CS reconstructed images at 1/100 & 1/11 undersampling rates and the iCS reconstructed images shown in Fig. 3.
It is demonstrated that the CNR is significantly improved by using the iCS method compared with the CS method at the same undersampling rate of 1/100 or the same acquisition time.
Table 1.
The average CNR values of the full k-space reference image, the CS reconstructed image at 1/100 & 1/11 undersampling rates and the iCS reconstructed image of each slice.
Figure 5.
The image error maps are calculated by subtracting the CS constructed image (a) and the iCS constructed image (b) from the full k-space reference image. This result shows a much reduced image error in the iCS reconstructed image over the conventional CS reconstructed image.
Table 2.
The average image error of the CS reconstructed image and the iCS reconstructed image compared with the full k-space reference image.