Inverse Singular Value Decomposition Research Articles

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.

Inverse estimation of indoor airflow patterns using singular value decomposition

The fast pace in the development of indoor sensors and communication technologies is allowing a great amount of sensor data to be utilized in various areas of indoor air applications, such as estimating indoor airflow patterns. The development of such an inverse model and the design of a sensor system to collect appropriate data are discussed in this study. Algebraic approaches, including singular value decomposition (SVD), are evaluated as methods to inversely estimate airflow patterns given limited sensor measurements. In lieu of actual sensor data, computational fluid dynamics data are used to evaluate the accuracy of the airflow patterns estimated by the inverse models developed in this study. It was found that the airflow patterns estimated by the linear inverse SVD model were as accurate as those estimated by the nonlinear inverse-multizone model. For the zones tested, sensor measurements along on the walls and near the inlet and outlet provided the greatest improvement in the accuracy of the estimated airflow patterns when compared with the results using measurements from other locations.