  In image denoising (IDN) processing, the low-rank property is usually
considered as an important image prior. As a convex relaxation approximation of
low rank, nuclear norm based algorithms and their variants have attracted
significant attention. These algorithms can be collectively called image domain
based methods, whose common drawback is the requirement of great number of
iterations for some acceptable solution. Meanwhile, the sparsity of images in a
certain transform domain has also been exploited in image denoising problems.
Sparsity transform learning algorithms can achieve extremely fast computations
as well as desirable performance. By taking both advantages of image domain and
transform domain in a general framework, we propose a sparsity transform
learning and weighted singular values minimization method (STLWSM) for IDN
problems. The proposed method can make full use of the preponderance of both
domains. For solving the non-convex cost function, we also present an efficient
alternative solution for acceleration. Experimental results show that the
proposed STLWSM achieves improvement both visually and quantitatively with a
large margin over state-of-the-art approaches based on an alternatively single
domain. It also needs much less iteration than all the image domain algorithms.
