A Robust Gradient-Based Algorithm to Correct Bias Fields of Brain MR Images

We developed a novel algorithm to estimate bias fields from brain magnetic resonance (MR) images using a gradient-based method. The bias field is modeled as a multiplicative and slowly varying surface. We fit the bias field by a low-order polynomial. The polynomial´s parameters are directly obtained by minimizing the sum of square errors between the gradients of MR images (both in the x-direction and y-direction) and the partial derivatives of the desired polynomial in the log domain. Compared to the existing retrospective algorithms, our algorithm combines the estimation of the gradient of the bias field and the reintegration of the obtained gradient polynomial together so that it is more robust against noise and can achieve better performance, which are demonstrated through experiments with both real and simulated brain MR images.