ABSTRACT
The quantitative validation of reconstruction algorithms requires reliable data. Rasterized simulations are popular but they are tainted by an aliasing component that impacts the assessment of the performance of reconstruction. We introduce analytical simulation tools that are suited to parallel magnetic resonance imaging and allow one to build realistic phantoms. The proposed phantoms are composed of ellipses and regions with piecewise-polynomial boundaries, including spline contours, Bézier contours, and polygons. In addition, they take the channel sensitivity into account, for which we investigate two possible models. Our analytical formulations provide well-defined data in both the spatial and k-space domains. Our main contribution is the closed-form determination of the Fourier transforms that are involved. Experiments validate the proposed implementation. In a typical parallel magnetic resonance imaging reconstruction experiment, we quantify the bias in the overly optimistic results obtained with rasterized simulations-the inverse-crime situation. We provide a package that implements the different simulations and provide tools to guide the design of realistic phantoms.
Subject(s)
Magnetic Resonance Imaging/instrumentation , Phantoms, Imaging , Algorithms , Brain/anatomy & histology , Computer Simulation , Fourier Analysis , Humans , Magnetic Resonance Imaging/methods , Models, Biological , Reproducibility of ResultsABSTRACT
In this work, we exploit the fact that wavelets can represent magnetic resonance images well, with relatively few coefficients. We use this property to improve magnetic resonance imaging (MRI) reconstructions from undersampled data with arbitrary k-space trajectories. Reconstruction is posed as an optimization problem that could be solved with the iterative shrinkage/thresholding algorithm (ISTA) which, unfortunately, converges slowly. To make the approach more practical, we propose a variant that combines recent improvements in convex optimization and that can be tuned to a given specific k-space trajectory. We present a mathematical analysis that explains the performance of the algorithms. Using simulated and in vivo data, we show that our nonlinear method is fast, as it accelerates ISTA by almost two orders of magnitude. We also show that it remains competitive with TV regularization in terms of image quality.
