Image decomposition combining low-rank and deep image prior

Most of the traditional variational decomposition models let the structure and texture belong to different functional spaces, which makes it difficult to distinguish structural edges from oscillatory components. Although existing learning-based methods can get better structural features, they require a large number of samples to train. However, image decomposition without ground truth is difficult to use supervised learning. Deep image prior is a typical unsupervised deep learning method, which avoids collecting a large number of training samples. Meanwhile, it is comparable to some of the most advanced methods in terms of image denoising, super-resolution, and inpainting. In this paper, we propose a new image decomposition model based on the deep image prior. Different from other existing methods, we use the deep image prior to characterize the cartoon and the low-rank norm to describe the texture. That is, our proposed model combines the superiority of the deep prior and sparsity. Moreover, we employ adaptive regularization parameters in order to make the structural component more edge-preserving. To the best of our knowledge, this is the first image decomposition model based on deep learning. To effectively solve the new model, the alternating direction method of multiplier is designed. In the numerical experiments, the structure images and texture images are displayed intuitively, and the structure images of the new model retain more edge features, and its texture images contain more complete texture details, thus verifying the validity of the new model.