Constrained reconstruction is making use of additional image information to improve the precision in the reconstruction of undersampled MR data. Here we use co-registered CT-data as an anisotropic diffusion constraint to improve sharpness in short T2* images reconstructed from undersampled 3D UTE data of a mummified human hand. The results are compared to other established reconstruction methods.
To show that the proposed reconstruction method improves image quality of undersampled data from a 3D UTE sequence, MR data of an ancient mummified human hand (ca. 1500-1100 BC, Fig. 1) with T2* relaxation times of 200-550 µs 2 was acquired. MR data were measured with a 3D UTE sequence on a 3T clinical scanner (Prisma Fit; SIEMENS Healthcare, Erlangen, Germany) with a custom build Rx/Tx solenoid coil using the following acquisition-parameters: FoV = 190 mm, Bandwidth = 2520 Hz/Pixel, TE = 70 µs, TR = 5 ms, α = 21 °, 4 averages, 12500 Spokes with 128 points per spoke. Additionally, high resolution (0.32x0.32x1 mm/Pixel) Dual Energy CT images (80 kV, 140 kV) of the specimen were acquired (SOMATOM; SIEMENS Healthcare, Erlangen, Germany). First, MR images were reconstructed with Kaiser-Bessel (KB) gridding and Hanning filtering onto a 192×192×192 matrix (undersampling factor 9.2). Subsequently, the CT images were aligned to the MR coordinate system using open source software (3D Slicer, version 4.5). Then, an iterative reconstruction using an anisotropic diffusion (AD) constraint3 based on co-registered CT data was used:
$$J(\boldsymbol\rho)=||\boldsymbol A\cdot\boldsymbol\rho - \boldsymbol y||^2 - \lambda_D\int\boldsymbol\rho\nabla(\boldsymbol D\nabla\boldsymbol\rho)\quad\text{with}\quad\boldsymbol D=\left(\boldsymbol 1-\frac{\boldsymbol g\cdot\boldsymbol g^T}{|\boldsymbol g|^2}/\sqrt{1+\boldsymbol g^2/a^2}\right)$$
where $$$\boldsymbol A$$$ denotes the system matrix that maps the image $$$\boldsymbol\rho$$$ to the raw data $$$\boldsymbol y$$$. In the regularization term the gradient operator $$$\boldsymbol g$$$ is applied to the CT image $$$(\boldsymbol g=\nabla Im_\mathrm{CT})$$$. The parameters $$$\lambda_D$$$ and $$$a$$$ were chosen to yield the best edge preservation in the image. The performance of the proposed AD reconstruction is compared to KB reconstruction and another iterative reconstruction, where $$$\boldsymbol D$$$ was set to the identity matrix, resulting in an unconstrained L2-based isotropic filter (L2).
Figure 2 shows an identical axial view across the middle of the metacarpal bones from the mummified hand for AD $$$(\lambda_D=0.1, a=10)$$$, L2 $$$(\lambda_D=0.1)$$$ and KB reconstructions. The CT data used for the AD constraint is also shown. The image reconstructed with anisotropic diffusion using a CT constraint retains sharper interfaces between tissues than conventional KB gridding or L2 reconstruction. Peak-to-peak values in the profile plots (Fig. 3) taken from the data along the indicated lines are used to quantify the improved sharpness of the image (Tab. 1). The profile plots for AD and KB reconstruction show the improvement of image sharpness for different structures in the specimen, where an increase in peak-to-peak values is associated with increased sharpness of the image (Fig. 3). In most of the analyzed structures AD reconstruction yields increased sharpness of up to 45% compared to KB reconstruction (Tab. 1). Except for the transition cortical bone – skin – air (III) where low contrast of the skin in CT images may be responsible for less selective edge preservation. In comparison with L2 reconstruction, AD reconstruction also shows an increase in sharpness, in one region of more than 50%. The AD reconstructed image yields reduced background noise in the area outside the object compared to the KB reconstructed image. However, no significant improvement of background noise can be seen when comparing AD to L2, since AD reconstruction behaves like L2 in areas of constant image values, which is the case for CT data outside of the hand.
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