Edge Preserving and Noise Reducing Reconstruction for Magnetic Particle Imaging

Abstract

Magnetic particle imaging (MPI) is an emerging medical imaging modality which is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. It is an important feature of MPI that even fast dynamic processes can be captured for 3D volumes. The high temporal resolution in turn leads to large amounts of data which have to be handled efficiently. But as the system matrix of MPI is non-sparse, the image reconstruction gets computationally demanding. Therefore, currently only basic image reconstruction methods such as Tikhonov regularization are used. However, Tikhonov regularization is known to oversmooth edges in the reconstructed image and to have only a limited noise reducing effect. In this work, we develop an efficient edge preserving and noise reducing reconstruction method for MPI. As regularization model, we propose to use the nonnegative fused lasso model, and we devise a discretization that is adapted to the acquisition geometry of the preclinical MPI scanner considered in this work. We develop a customized solver based on a generalized forward-backward scheme which is particularly suitable for the dense and not well-structured system matrices in MPI. Already a non-optimized prototype implementation processes a 3D volume within a few seconds so that processing several frames per second seems amenable. We demonstrate the improvement in reconstruction quality over the state-of-the-art method in an experimental medical setup for an in-vitro angioplasty of a stenosis.

Image reconstruction for Magnetic Particle Imaging using an Augmented Lagrangian Method

“…A drive field was applied to move the FFL in the direction orthogonal to it. Then, the received signal at each rotation angle was calculated using [7,13]:…”

“…Typically, this inverse problem is solved via iterative regularized methods such as the Kaczmarz method, also known as Algebraic Reconstruction Technique (ART) [5]. Nonnegative fused lasso model, which minimizes the total variation and l1 norm solution, is reported to perform better for preserving edge discontinuities in the image [7].…”

“…In MPI, the FFR is typically characterized as a small ellipsoidal volume, which is called a Field Free Point (FFP) [1][2][3][4][5][6][7]. As the received signal is directly related to the number of particles in the FFR, field free line (FFL) imaging is proposed to increase sensitivity via using a larger FFR volume [8].…”

“…We use two different approaches to solve the convex problem described by the LSE. In the first one, we use a formulation minimizing total variation (TV) and l1 norm [12], similar to the nonnegative fused lasso model [7]. In the second one, we solve a regularized least square problem formulation, which is considered as the state-of-theart reconstruction method in MPI [7].…”

“…In the first one, we use a formulation minimizing total variation (TV) and l1 norm [12], similar to the nonnegative fused lasso model [7]. In the second one, we solve a regularized least square problem formulation, which is considered as the state-of-theart reconstruction method in MPI [7]. We compare these two formulations by using a hybrid Alternating Direction Method of Multipliers (ADMM) solution for the former, and ART solution for the latter, in terms of image quality and convergence time for various SNR values.…”