Simultaneous correction of sensitivity and spatial resolution in projection‐based magnetic particle imaging
Authors: Murase Kenya 
Published: January 2020

Purpose

The purpose of this study was to develop a method to simultaneously correct the spatial resolution and inhomogeneous sensitivity of a receiving coil in projection‐based magnetic particle imaging — and to investigate its efficacy through simulation and experimental studies.

Methods

Magnetic particle imaging (MPI) images were reconstructed using the simultaneous algebraic reconstruction technique (SART), and simultaneous corrections to sensitivity and spatial resolution were performed by incorporating the sensitivity map of the receiving coil and the system function into the SART algorithm. After each SART update, the regularization method — with total variation (TV) minimization — was used to suppress noise amplification and artifact generation. For comparison, MPI images were also reconstructed using the filtered backprojection (FBP) method and the FBP‐truncated singular value decomposition (TSVD) method, in which the system function was deconvolved from the projection data using TSVD. In simulation studies, the sensitivity map of a second‐order, gradiometer‐type receiving coil was generated using the Biot–Savart law, while the system function was obtained by calculating the MPI signals induced by magnetic nanoparticles at various distances from a field‐free line (FFL), using a lock‐in‐amplifier model. The effects of a regularization parameter for TV minimization (α), number of iterations (N), and signal‐to‐noise ratio (SNR) of the MPI signals on the reconstructed MPI images of a numerical phantom were evaluated, using the image profiles and percent root mean square error (PRMSE). Experimental studies involved the calculation of the system function using a tube phantom. Projection data for an A‐shaped phantom were acquired using our MPI scanner, and their MPI images were reconstructed from the projection data, as described above.

Results

When both the sensitivity and spatial resolution were corrected (SART‐SR), the quality of the reconstructed images was seen to have improved, compared to when the spatial resolution was not corrected — or when the FBP and FBP‐TSVD methods were used. When SNR was low (20), a larger α value yielded a better image. The minimum PRMSE occurred at N ≈ 200–400 and increased with increasing N thereafter. When SNR was high (100), the image quality was generally not dependent on the α value within its studied range. The PRMSE decreased slowly with increasing N, and tended to converge to a constant value. The full width at half maximum (FWHM) of the profile was obtained from the A‐shaped phantom, reconstructed using the SART‐SR algorithm with α = 0.05 and N = 1000. The FWHM value of the tube (2 mm diameter) in the A‐shaped phantom image was found to be 2.2 mm on average, whereas those calculated from the images obtained by the FBP and FBP‐TSVD methods were 4.4 and 3.0 mm on average, respectively. Spatial resolution improved when using the FBP‐TSVD method as compared to the FBP method but image distortion and artifacts were observed.

Conclusions

Although further studies are necessary to optimize the parameters used in the SART algorithm and in TV minimization, the present results suggest that the proposed method is useful for improving the image quality of projection‐based MPI.