An Image Denoising Algorithm Based on Singular Value Decomposition and Non-local Self-similarity

Image denoising is a basic but important step in image preprocessing, computer vision, and related areas. Based on singular value decomposition (SVD) and non-local self-similarity, This paper proposed an image denoising algorithm which is simple in computation. The proposed algorithm is divided into three steps: firstly, the block matching technique is used to find similar patches to construct one matrix, which is of low rank; secondly, SVD is performed on this matrix, and the singular value matrix is processed by principal component analysis (PCA); finally, all similar patches are aggregated to retrieve the denoised image. Since the noise in the image will affect the computation of similar patches, this procedure is iterated many times to enhance the performance. Simulated experiments on different images show that the proposed algorithm performs well in denoising images. Compared with most denoising algorithms, the proposed algorithm is of high efficiency.