A new variational image restoration applied to 3D angiographies

We propose a new variational restoration method. We express the energy as the sum of a data attachment term. A contour smoothing term and an enhancement term. The contour smoothing is achieved by minimizing the square of the derivative of the intensity in the contour direction. The enhancement is obtained by minimizing the square of the gradient norm in each estimated region, and acts like shock filters. The minimization of the energy is then done using the conjugate gradient algorithm. We present an algorithm which allows us to compute easily the gradient of the energy in the discrete case, without calculating the Euler-Lagrange equations. Experiments have been carried out on both synthetic and real images applied to 3D angiographies.