Deep image prior and weighted anisotropic-isotropic total variation regularization for solving linear inverse problems

Deep learning, particularly unsupervised techniques, has been widely used to solve linear inverse problems due to its flexibility. A notable unsupervised approach is the deep image prior (DIP), which employs a predetermined deep neural network to regularize inverse problems by imposing constraints on the generated image. This article introduces an optimization technique (DIP-AITV) by combining the DIP with the weighted anisotropic-isotropic total variation (AITV) regularization. Furthermore, we utilize the alternating direction method of multipliers (ADMM), a highly flexible optimization technique, to solve the DIP-AITV minimization problem effectively. To demonstrate the benefits of the proposed DIP-AITV method over the state-of-the-art DIP, DIP-TV, DIP-WTV and CS-DIP, we solve two linear inverse problems, i.e., image denoising and compressed sensing. Computation examples on the MSE and PSNR values show that our method outperforms the existing DIP-based methods in both synthetic and real grayscale and color images.