Marcus Björk1, Dave Zachariah1, Joel Kullberg2, Petre Stoica1. 1. Department of Information Technology, Uppsala University, Uppsala, Sweden. 2. Department of Radiology, Uppsala University, Uppsala, Sweden.
Abstract
PURPOSE: Models based on a sum of damped exponentials occur in many applications, particularly in multicomponent T2 relaxometry. The problem of estimating the relaxation parameters and the corresponding amplitudes is known to be difficult, especially as the number of components increases. In this article, the commonly used non-negative least squares spectrum approach is compared to a recently published estimation algorithm abbreviated as Exponential Analysis via System Identification using Steiglitz-McBride. METHODS: The two algorithms are evaluated via simulation, and their performance is compared to a statistical benchmark on precision given by the Cramér-Rao bound. By applying the algorithms to an in vivo brain multi-echo spin-echo dataset, containing 32 images, estimates of the myelin water fraction are computed. RESULTS: Exponential Analysis via System Identification using Steiglitz-McBride is shown to have superior performance when applied to simulated T2 relaxation data. For the in vivo brain, Exponential Analysis via System Identification using Steiglitz-McBride gives an myelin water fraction map with a more concentrated distribution of myelin water and less noise, compared to non-negative least squares. CONCLUSION: The Exponential Analysis via System Identification using Steiglitz-McBride algorithm provides an efficient and user-parameter-free alternative to non-negative least squares for estimating the parameters of multiple relaxation components and gives a new way of estimating the spatial variations of myelin in the brain.
PURPOSE: Models based on a sum of damped exponentials occur in many applications, particularly in multicomponent T2 relaxometry. The problem of estimating the relaxation parameters and the corresponding amplitudes is known to be difficult, especially as the number of components increases. In this article, the commonly used non-negative least squares spectrum approach is compared to a recently published estimation algorithm abbreviated as Exponential Analysis via System Identification using Steiglitz-McBride. METHODS: The two algorithms are evaluated via simulation, and their performance is compared to a statistical benchmark on precision given by the Cramér-Rao bound. By applying the algorithms to an in vivo brain multi-echo spin-echo dataset, containing 32 images, estimates of the myelin water fraction are computed. RESULTS: Exponential Analysis via System Identification using Steiglitz-McBride is shown to have superior performance when applied to simulated T2 relaxation data. For the in vivo brain, Exponential Analysis via System Identification using Steiglitz-McBride gives an myelin water fraction map with a more concentrated distribution of myelin water and less noise, compared to non-negative least squares. CONCLUSION: The Exponential Analysis via System Identification using Steiglitz-McBride algorithm provides an efficient and user-parameter-free alternative to non-negative least squares for estimating the parameters of multiple relaxation components and gives a new way of estimating the spatial variations of myelin in the brain.
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