Image restoration via wavelet-based low-rank tensor regularization

Low-rank models have been widely applied for visual analysis. However, the conventional global low rank on a single whole image and the patch-level low rank have difficulty in perfectly preserving dependence (or correlation) and the latent structures in the image. Inspired by recent advances in low-rank tensor analysis, a wavelet-based low rank tensor regularization model (WLTR) is proposed in this work. Utilizing the fact that the coefficients of an image under wavelet transform exhibit sparsity, the low-rank regularization can be obtained by imposing the nuclear norm constraint on the tensor composed of wavelet subbands coefficients. Considering all structure information of intrascale and interscale coefficients under the tensor representation, the proposed method characterizes the local and global elements in a unified manner. To make the proposed WLTR tractable and robust, the alternative direction of multiplier method (ADMM) is adopted to efficiently and effectively solve this convex optimization problem. Extensive experiments on various types of image restoration problems, including inpainting, deblurring and denoising, validate WLTR outperforms several existing state-of-the-art approaches in terms of peak signal-to-noise ratio and visual quality.