Abstract: Blind image restoration is to recover the original images from the blurred images when the blurring function in the image formation process is unknown. In this paper, we present an efficient and practical blind image restoration algorithm based on total variational (TV) regularization. The TV regularization employs TV norm on the images for the smoothness constraint, while the traditional regularization uses H$+1$/ norm for the smoothness constraint. The TV regularization provides a larger functional space for the image functions and is known for allowing discontinuities in the image function to be recovered. The blur functions considered in this paper are combinations of a Gaussian defocus blur and a uniform motion blur, that each can be approximated by a parametric function of one or two parameters. The use of this parametric form intrinsically imposes a constraint on the blur function. The small number of parameters involved in the parametric blur function makes the resulting optimization problem tractable. The above formulation for the restoration from a single image is then extended to the blind restoration from an image sequence by introducing motion parameters into the multi-frame data constraints. An iterative alternating numerical algorithm is developed to solve the nonlinear optimization problems. Each iteration of the alternating numerical algorithm involves the Fourier preconditioned conjugate gradient iterations to update the restored image and quasi-Newton steps to update the blur and motion parameters. Some experimental results are shown to demonstrate the usefulness of our algorithm. !15
展开▼
