RF inhomogeneities correction inMRIT-weighted spin-echo image handling the non-multiplicative character of the bias field

We propose a method to reduce the noise and to eliminate the effects of the inhomogeneity of the Radio-Frequency (RF) pulses and of the sensivity of the RF reception, particularly in the case of MR T-weighted images acquired with a low-field MRI system. In T-weighted images the effects of the pulse inhomogeneities vary with the tissues. Consequently the bias field is not strictly multiplicative and depends on the content of the image. In our approach, the MR signal is modeled as a sum of contributions of all the tissues present in the object. For the sake of generality, each pixel is assumed to contain an unknown proportion of each tissue, which thereby enables the method to cope with partial volume effect. The number of tissues composing the object as well as the MR characteristics of each tissue are assumed known. Several images with different acquisition parameter values are also needed. A penalized least-square criterion is proposed to estimate the RF emitted field, the RF sensitivity reception and the proportion of each tissue. The criterion incorporates smoothness regularization terms for both RF fields and for the proportion of each tissue in a view to reduce noise. We solve the optimization problem using a conjugate gradient algorithm within a block coordinate descent iterative scheme. Results based on simulation and on real MR images of fish acquired on a 0.2 T MRI demonstrate the effectiveness of the method.