An image denoising algorithm based on adaptive clustering and singular value decomposition

Abstract

Abstract Self‐similarity, a prior of natural images, has attracted much attention. The attribute means that low‐rank group matrices can be constructed from similar image patches. For low‐rank approximation denoising methods based on singular value decomposition (SVD) the ability to accurately construct group matrices with noise and handle singular values are keys. Here, combining image priors, a two‐stage clustering method to adaptively construct group matrices is designed. The method is anti‐noise, that is, when noise levels are high, these matrices are more accurate than that constructed by other algorithms. Then, according to the significance of singular values and singular vectors, singular vectors of the low‐rank estimations are corrected so that the residual noise in the low‐rank estimations is further suppressed. For back projection , the authors use the original noise level and the residual image to adaptively determine projection parameters and new noise levels . So, authors' back projection can provide a good foundation for authors' two‐stage denoising methods, better remove noise and preserve image details. Experimental results show that compared with the existing state‐of‐the‐art denoising algorithms, the proposed algorithm achieves competitive denoising performances in terms of quantitative metrics and preserving details. Especially with the increase of noise, the competitiveness of authors' algorithms is gradually enhanced.

Keywords

• Interpolation and function approximation (numerical analysis)
• Linear algebra (numerical analysis)
• Integral transforms in numerical analysis
• Optical, image and video signal processing
• Interpolation and function approximation (numerical analysis)
• Linear algebra (numerical analysis)