EPFL | Biomedical Imaging Group | Analytical Phantoms

Realistic Analytical Phantoms for Parallel Magnetic Resonance Imaging

M. Guerquin-Kern, L. Lejeune, K.P. Pruessmann, M. Unser

IEEE Transactions on Medical Imaging, vol. 31, no. 3, pp. 626–636, March 2012.

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.

Erratum

p. 630, second column, Equation (24), a factor (1 ∕ ||ω||²) is missing at the beginning of the right-hand side of the equation. The corrected equation should read g_𝓑^α(ω) = (1 ∕ ||ω||²) ∑_{n = 0}^{N − 1} e^{−j ω · r_n} ∑_{i = 0}^{2 |α| + 1} d_{n, i} h⁽ⁱ⁾(ω · β_n, ω · γ_n)

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AUTHOR="Guerquin-Kern, M. and Lejeune, L. and Pruessmann, K.P. and
	Unser, M.",
TITLE="Realistic Analytical Phantoms for Parallel Magnetic Resonance
	Imaging",
JOURNAL="{IEEE} Transactions on Medical Imaging",
YEAR="2012",
volume="31",
number="3",
pages="626--636",
month="March",
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