RegularizedLeastSquares.jl: Modality Agnostic Julia Package for Solving Regularized Least Squares Problems

Abstract

Image reconstruction in Magnetic Particle Imaging (MPI) is an ill-posed linear inverse problem. A standard method
for solving such a problem is the regularized least squares approach, which uses, a regularization function to
reduce the impact of measurement noise in the reconstruced image by leveraging prior knowledge. Various
optimization algorithms, including the Kazcmarz method or the Alternating Direction Method of Multipliers
(ADMM), and regularization functions, such as l2 or Fused Lasso priors have been employed. Therefore, the
creation and implementation of cutting-edge image reconstruction techniques necessitate a robust and adaptable
optimization framework. In this work, we present the open-source Julia package RegularizedLeastSquares.jl, which
provides a large selection of common optimization algorithms and allows flexible inclusion of regularization
functions. These features enable the package to achieve state-of-the-art image reconstruction in MPI