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Utilization Of Fractional Brownian Motion In Constrained Least-Squares Restoration Of Medical Images

Constrained least-squares techniques have been used to produce a well known class of image restoration algorithms. These techniques typically involve minimizing a linear operator on a vector representation of an image, subject to a constraint. For cases where an equality constraint is appropriate the method of Lagrange multipliers can be used to produce a restored image. In this work a fractal textural model,fractional Brownian motion, is used to represent images of interest. Using a variance fractal dimension estimator a non-linear operator, that represents the squared difference between the fractal dimension of the restored image and an a priori value is minimized, subject to the constraint that the norm of the residual between the restored image and available measurement equal the norm of the additive noise.