  The data-driven sparse methods such as synthesis dictionary learning (e.g.,
K-SVD) and sparsifying transform learning have been proven effective in image
denoising. However, they are intrinsically single-scale which can lead to
suboptimal results. We propose two methods developed based on wavelet subbands
mixing to efficiently combine the merits of both single and multiscale methods.
We show that an efficient multiscale method can be devised without the need for
denoising detail subbands which substantially reduces the runtime. The proposed
methods are initially derived within the framework of sparsifying transform
learning denoising, and then, they are generalized to propose our multiscale
extensions for the well-known K-SVD and SAIST image denoising methods. We
analyze and assess the studied methods thoroughly and compare them with the
well-known and state-of-the-art methods. The experiments show that our methods
are able to offer good trade-offs between performance and complexity.
