2.5 Results
4.3.2 Method
The approach estimates using N4 a coherent and smooth bias field (step (IX) in Figure 4.1) from the reconstructed image, which is then propagated to each slice of the scans using the estimated motion and each slice is corrected (step (X) in Figure 4.1). N4 is employed as it requires no a priori knowledge and has shown to be relatively performant in a variety of imaging acquisition strategies. It assumes that the bias field has a multiplicative model where the formation of an MR image is:
X(i ) = UH R(i ) × IH R(i ) + n(i ), (4.2)
where X is the intensity in the reconstructed image, IH Ris the bias field inhomogeneity, UH R is the true intensity and n is the noise. The bias field is estimated in the log space, making the model additive:
log(X − n) = log(UH R)+ log(IH R),
log(UH R) = log(X − n)− log(IH R). (4.3)
(VIII) Brain Mask Refinement (VII)
TV Super-Resolution (I) Brain Localization and
Extraction
(VI) Motion Estimation
Stacks of Thick Slices
(Clinical MR scans)
HR reconstructed image
(V)
Intensity Rescaling in [0,255]
(II) Inter-Slice Intensity Mean
Shift Correction
(IV) Brain Histogram Equalization
(IX) Global Bias Field Estimation
(X) Slice-by-Slice Bias Field
Correction (III) Slice-by-Slice Bias Field Estimation and Correction
Figure 4.1 – Reconstruction pipeline for fetal MRI using the proposed bias field correction method. The approach takes advantage of the reconstruction framework to provide a recon- structed image free of smooth bias field inhomogeneities. New processes involved in the reconstruction pipeline are highlighted in red. Step (IX) estimates a coherent and smooth bias field from the image reconstructed at step (VII) using N4 [5], which is then propagated to each slice of the scans using the motion estimated at step (VI) and used to correct bias field inhomogeneity in each slice (Step (X)). Our solution is thus able to take into account inter-slice motion and to correct for the smooth bias field. Note that the previous independent slice-by-slice bias field correction is performed at the first loop (Step (III)) since the method is dependent on the preceding motion estimation and super-resolution steps.
4.3. Slice-by-slice intensity inhomogeneity correction from a globally-estimated bias field
The N4 method seeks iteratively the smooth multiplicative field that maximizes the high frequency content of the distribution of tissue intensity. Specifically, N4 performs a bias correction step on the corrected image from the previous iteration to estimate the residual bias field. As it is designed to converge such that the residual bias field tends to 0, the total bias field estimated at iteration n became the sum of the first n residual bias field. Once the bias field IH Ris estimated from the reconstructed image, the bias field ILRkl of each slice of the scans is generated through the propagation of IH R using the forward model of the super-resolution problem:
ILRkl = HklIH R, (4.4)
and each slice Yklis corrected from its bias field:
ULRkl(i ) = Ykl(i )/ILRkl. (4.5)
Therefore, the global bias field can be more coherently corrected slice-by-slice, accounting for possible inter-slice motions, which results in the reconstruction of images free of the smooth bias field. A proof of concept will be provided in the next section.
4.3.3 Results
To illustrate the improvement in reconstruction quality, we will show in this section the reconstruction results we obtained for one specific subject diagnosed with unilateral ventricu- lomegaly, illustrative of all. Acquisition was performed during the 26t hweek GA at Boston Children’s Hospital, Boston, USA, using a 3T Siemens Skyra with a T2-weighted HASTE se- quence (TE/TR = 116-119/1600ms). The dataset is formed by 6 orthogonal scans of thick slices, two per anatomical direction, with an anisotropic resolution of 1 × 1 × 2mm3. An HR image has been reconstructed using (1) the previous pipeline where independent slice-by-slice bias field estimation and correction were performed (see Chapter 2 for more details) and (2) the new pipeline integrating our coherent slice-by-slice bias field correction approach (Figure 4.1). Figure 4.2 shows the reconstruction results as well as the bias fields estimated using the two different approaches.
Visual inspection shows clearly that our method allows the estimation of a coherent bias field (c) which provides a reconstructed image quasi free of smooth intensity inhomogenities. It can also be observed that the uncohenrency of the bias field used previously introduces intensity artifacts that are removed with the new approach. This new pipeline will be adopted in the rest of the works presented in this chapter.
Chapter 4. Further Improvements (a) (b) (c) (d) (e)
Figure 4.2 – Visual comparison of reconstruction results obtained using the previous and the improved slice-by-slice bias field correction methods. (a) presents one of the original acquired scan. (b) presents the bias field estimated independently slice by slice using the previous method. (c) presents the bias field estimated using the improved method and projected into the space of the scan. (d) presents the HR image reconstructed when using the previous bias field correction method. (e) presents the HR image reconstructed when using the improved method. It can be observed that the proposed method allow the estimation of a coherent bias field (c) which provides a reconstructed image quasi free of smooth intensity inhomogenities. It can also be observed that the uncoherency of the bias field used previously introduces intensity artifacts that are removed with the new approach.