An L-curve approach to optimal determination of regularization parameter in image restoration

Image restoration refers to the problem of removal or reduction of degradation in noisy blurred images. The image degradation is usually modeled by a linear blur and an additive white noise process, and an image restoration problem can then be considered as an integral equation of the first kind. In many practical image restoration problems, the linear blur involved are always ill-conditioned. This provides a typical example for ill-posed problems for which the solutions are unstable. The method of regularization provides stable solutions to image restoration problems with a tradeoff between accuracy and smoothness of the solutions. The tradeoff is determined by a regularization parameter. In this paper, an L-curve approach to determining this tradeoff is proposed. It is demonstrated that a regularization parameter corresponding to the largest curvature of the L-curve gives a nearly optimal regularized solution of a given image restoration problem