Estimation of image bias field with sparsity constraints

We propose a new scheme to estimate image bias field through introducing two sparsity constraints. One is that the bias-free image has concise representation with image gradients or coefficients of other image transformations. The other constraint is that model fit on the bias field should be as concise as possible. The new scheme enables adaptive specifications of the estimated bias field's smoothness, and results in extremely accurate solutions with more efficient optimization techniques, e.g. linear programming. These distinguish our approaches from many previous methods. Our techniques can be applied to intensity inhomogeneity correction of medical images, illumination and vignetting estimation of images captured by digital cameras.