Half-quadratic regularization for MRI image restoration

We consider the reconstruction of MRI images by minimizing regularized cost-functions. To accelerate the computation of the estimate, two forms of half-quadratic regularization, multiplicative and additive, are often used. In Nikolova and Ng (2002), we have compared both theoretically and experimentally the efficiency of these two forms using one-dimensional signals. The goal of this paper is to compare experimentally the efficiency of these two forms using MRI image reconstruction. We find that using the additive form is more computationally effective than using the multiplicative form.