Joint image denoising using adaptive principal component analysis and self-similarity

The non-local means (NLM) has attracted enormous interest in image denoising problem in recent years. In this paper, we propose an efficient joint denoising algorithm based on adaptive principal component analysis (PCA) and self-similarity that improves the predictability of pixel intensities in reconstructed images. The proposed algorithm consists of two successive steps without iteration: the low-rank approximation based on parallel analysis, and the collaborative filtering. First, for a pixel and its nearest neighbors, the training samples in a local search window are selected to form the similar patch group by the block matching method. Next, it is factorized by singular value decomposition (SVD), whose left and right orthogonal basis denote local and non-local image features, respectively. The adaptive PCA automatically chooses the local signal subspace dimensionality of the noisy similar patch group in the SVD domain by the refined parallel analysis with Monte Carlo simulation. Thus, image features can be well preserved after dimensionality reduction, and simultaneously the noise is almost eliminated. Then, after the inverse SVD transform, the denoised image is reconstructed from the aggregate filtered patches by the weighted average method. Finally, the collaborative Wiener filtering is used to further remove the noise. The experimental results validate its generality and effectiveness in a wide range of the noisy images. The proposed algorithm not only produces very promising denoising results that outperforms the state-of-the-art methods in most cases, but also adapts to a variety of noise levels.