A parametric gradient descent MRI intensity inhomogeneity correction algorithm

Given an appropriate imaging resolution, a common Magnetic Resonance Imaging (MRI) model assumes that the object under study is composed of homogeneous tissues whose imaging intensity is constant, so that MRI produces piecewise constant images. The intensity inhomogeneity (IIH) is modeled by a multiplicative inhomogeneity field. It is due to the spatial inhomogeneity in the excitatory Radio Frequency (RF) signal and other effects. It has been acknowledged as a greater source of error for automatic segmentation algorithms than additive noise. We propose a parametric IIH correction algorithm for MRI that consists of the gradient descent of an error function related to the classification error of the IIH corrected image. The inhomogeneity field is modeled as a linear combination of 3D products of Legendre polynomials. In this letter we test both the image restoration capabilities and the classification accuracy of the algorithm. In restoration processes the adaptive algorithm is used only to estimate the inhomogeneity field. Test images to be restored are IIH corrupted versions of the BrainWeb site simulations. The algorithm image restoration is evaluated by the correlation of the restored image with the known clean image. In classification processes the algorithm is used to estimate both the inhomogeneity field and the intensity class means. The algorithm classification accuracy is tested over the images from the IBSR site. The proposed algorithm is compared with Maximum A Posteriori (MAP) and Fuzzy Clustering algorithms.