Image denoising via sparse and redundant representations over learned dictionaries in wavelet domain

This paper proposes a novel hybrid image denoising method based on wavelet transform and sparse and redundant representations model which is called signal-scale wavelet K-SVD algorithm (SWK-SVD). In wavelet domain, mutiscale features of images and sparse prior of wavelet coefficients are achieved in a natural way. This gives us the motivation to build sparse representations in wavelet domain. Using K-SVD algorithm, we obtain adaptive and over-complete dictionaries by learning on image approximation and high-frequency wavelet coefficients respectively. This leads to a state-of-art denoising performance both in PSNR and visual effects with strong noise.