  Spatially-varying intensity noise is a common source of distortion in medical
images. Bias field noise is one example of such a distortion that is often
present in the magnetic resonance (MR) images or other modalities such as
retina images. In this paper, we first show that the bias field noise can be
considerably reduced using Empirical Mode Decomposition (EMD) technique. EMD is
a multi-resolution tool that decomposes a signal into several principle
patterns and residual components. We show that the spatially-varying noise is
highly expressed in the residual component of the EMD and could be filtered
out. Then, we propose two hierarchical multi-resolution EMD-based algorithms
for robust registration of images in the presence of spatially varying noise.
One algorithm (LR-EMD) is based on registration of EMD feature-maps from both
floating and reference images in various resolution levels. In the second
algorithm (AFR-EMD), we first extract an average feature-map based on EMD from
both floating and reference images. Then, we use a simple hierarchical
multi-resolution algorithm to register the average feature-maps. For the brain
MR images, both algorithms achieve lower error rate and higher convergence
percentage compared to the intensity-based hierarchical registration.
Specifically, using mutual information as the similarity measure, AFR-EMD
achieves 42% lower error rate in intensity and 52% lower error rate in
transformation compared to intensity-based hierarchical registration. For
LR-EMD, the error rate is 32% lower for the intensity and 41% lower for the
transformation. Furthermore, we demonstrate that our proposed algorithms
improve the registration of retina images in the presence of spatially varying
noise.
