Retrospective correction of intensity inhomogeneity with sparsity constraints in transform-domain: Application to brain MRI

Abstract

An effective retrospective correction method is introduced in this paper for intensity inhomogeneity which is an inherent artifact in MR images. Intensity inhomogeneity problem is formulated as the decomposition of acquired image into true image and bias field which are expected to have sparse approximation in suitable transform domains based on their known properties. Piecewise constant nature of the true image lends itself to have a sparse approximation in framelet domain. While spatially smooth property of the bias field supports a sparse representation in Fourier domain. The algorithm attains optimal results by seeking the sparsest solutions for the unknown variables in the search space through L1 norm minimization. The objective function associated with defined problem is convex and is efficiently solved by the linearized alternating direction method. Thus, the method estimates the optimal true image and bias field simultaneously in an L1 norm minimization framework by promoting sparsity of the solutions in suitable transform domains. Furthermore, the methodology doesn't require any preprocessing, any predefined specifications or parametric models that are critically controlled by user-defined parameters. The qualitative and quantitative validation of the proposed methodology in simulated and real human brain MR images demonstrates the efficacy and superiority in performance compared to some of the distinguished algorithms for intensity inhomogeneity correction.