Relaxation Time Estimation from Complex Magnetic Resonance Images

Abstract

Magnetic Resonance (MR) imaging techniques are used to measure biophysical properties of tissues. As clinical diagnoses are mainly based on the evaluation of contrast in MR images, relaxation times assume a fundamental role providing a major source of contrast. Moreover, they can give useful information in cancer diagnostic. In this paper we present a statistical technique to estimate relaxation times exploiting complex-valued MR images. Working in the complex domain instead of the amplitude one allows us to consider the data bivariate Gaussian distributed, and thus to implement a simple Least Square (LS) estimator on the available complex data. The proposed estimator results to be simple, accurate and unbiased.

Denoising High-field Multi-dimensional MRI with Local Complex PCA

“…One of the main drawbacks of existing local PCA methods for denoising is that they work on magnitude images, which follow Rician distributions. A simple correction proposed in (Baselice et al, 2009;Eichner et al, 2016) for removing the Rician bias in DWI averaging is to revert to the complex signal, taking into account the phase information. Phase contains additional variations due to non-local effects of air cavities around the brain, which bring severe ringing artifacts in the reconstructed data ( Fig.2A).…”

Improved estimation of MR relaxation parameters using complex‐valued data

“…Estimators based on complex-valued data have been shown to be efficient, that is, they are unbiased and the variance of the estimated parameters equals the lowest possible variation theoretically possible, as predicted by the Cramer-Rao Lower bounds (CRLB) (11,12,14,30). The CRLB derived for T 1 estimation in (11) does not generalize for the Look-Locker sequence addressed here.…”

“…In the past few years, methods to estimate T 1 , T 2 , and T Ã 2 parameters directly from complex-valued data have been introduced by our group (10) and others (11)(12)(13)(14)(15). These novel methods demonstrate the improved bias-variance performance of estimators based on complex-valued data over a limited set of magnitude-based estimators.…”

Spatially regularized estimation of the tissue homogeneity model parameters in DCE‐MRI using proximal minimization

“…where is a single measured element of ( voxel, time sample) and is the true value, not distorted by the noise . The noise follows the signal‐dependent Rice distribution, assuming Cartesian imaging for simplicity. Major mathematical notations used throughout the paper can be found in Table .…”

“…The values in S can be described by the model where S i,n is a single measured element of S (i th voxel, n th time sample) and S i,n is the true value, not distorted by the noise i,n . The noise follows the signal-dependent Rice distribution, 35 (1)…”