Modeling the Image Reconstruction Problem in MPI

In this work, we develop a new operator-based approach for MPI image reconstruction that can directly map arbitrary time domain data into images. The method enables efficient, rapid, and accurate image reconstruction using a diversity of transmit and receiver coils while making minimal assumptions regarding the underlying physics. The system model maps the underlying image, x, to the acquired time domain signal, b, by a sequence of 4 linear matrix operators given by A = GVEH. We then solve for x in a system model b = Ax + n, where n is a noise term, using standard approaches such as regularized least squares. The operator H is derived from the Langevin model and is a combination of convolutional operators, E is a row selector matrix that selects the field accessible point (FFP) at each measured time point, V is related to the FFP velocity at each time point, and G incorporates the system filter of the transmit signal. Each of these operators can be implemented efficiently as matrix-vector products, which makes the inverse problem computationally tractable. The method also enables simultaneous application of physical information such as non-negativity constraints and smoothness. Initial results show that our approach effectively and efficiently reconstructs 2D images from simulated and experimental data for multiple transmit and receiver coils. This approach provides a pathway for significantly reducing the computational pipeline of future MPI systems, and it will allow for greater flexibility in MPI scanner design. The current model does not include any nanoparticle relaxation effects and assumes a homogenous B-field. Incorporating these components is planned for future work.&nbsp