A Variational Model for Image Restoration under Blur and Noise using Nuclear Norm regularization

Blur and noise are intrinsic factors that develop during the image acquisition process and poses a limitation on the image acquisition system. Denoising and deconvolution are a class of image processing algorithms that aim to recover these spatially blurred and noisy images. Both the algorithms have their own merits and drawbacks, with denoising primarily focusing on noise removal and deconvolution on blur removal. In this paper, we propose a variational formulation for applying denoising and deconvolution jointly on an acquired image. We make use of the nuclear norm of Hessian as the regularizer and solve the resultant optimization problem using primal dual hybrid gradient descent algorithms. Comparison with multiple classical techniques, for different image degradation scenarios, justifies the merit of using such a joint denoising-deconvolution scheme for image restoration.