Variational models involving Euler's elastica energy have a wide range of applications in digital image processing. Recently, fast methods, such as the proximal-augmented Lagrangian method (PALM), have been successfully used to solve nonlinear higher order models for image restoration. In this paper, we extend fast method PALM to Euler's elastica deconvolution models with quadratic and nonquadratic fidelity terms. The proposed variational model can eliminate blur and noise and preserve edges while reducing the blocky and staircase artifacts during image restoration. We present an efficient and effective solution to the proposed minimization problems by a proximal-based numerical scheme. Our numerical experiments demonstrate several results on image deblurring and denoising, which shows a clear improvement of the proposed model over standard variational models such as total variation and Hessian-based model.
