Statistical Inference Using GLEaM Model with Spatial Heterogeneity and Correlation between Regions

A better understanding of the various patterns in the coronavirus disease 2019 (COVID-19) spread in different parts of the world is crucial to its prevention and control. Motivated by the celebrated GLEaM model (Balcan et al., 2010 [1]), this paper proposes a stochastic dynamic model to depict the evolution of COVID-19. The model allows spatial and temporal heterogeneity of transmission parameters and involves transportation between regions. Based on the proposed model, this paper also designs a two-step procedure for parameter inference, which utilizes the correlation between regions through a prior distribution that imposes graph Laplacian regularization on transmission parameters. Experiments on simulated data and real-world data in China and Europe indicate that the proposed model achieves higher accuracy in predicting the newly confirmed cases than baseline models.

Pointwise Mutual Information based Graph Laplacian Regularized Sparse Unmixing

Sparse unmixing (SU) aims to express the observed image signatures as a linear combination of pure spectra known a priori and has become a very popular technique with promising results in analyzing hyperspectral images (HSI) over the past ten years. In SU, utilizing the spatial-contextual information allows for more realistic abundance estimation. To make full use of the spatial-spectral information, in this letter, we propose a pointwise mutual information (PMI) based graph Laplacian regularization for SU. Specifically, we construct the affinity matrices via PMI by modeling the association between neighboring image features through a statistical framework, and then we use them in the graph Laplacian regularizer. We also adopt a double reweighted $\ell_{1}$ norm minimization scheme to promote the sparsity of fractional abundances. Experimental results on simulated and real data sets prove the effectiveness of the proposed method and its superiority over competing algorithms in the literature.

Pointwise Mutual Information based Graph Laplacian Regularized Sparse Unmixing

Sparse unmixing (SU) aims to express the observed image signatures as a linear combination of pure spectra known a priori and has become a very popular technique with promising results in analyzing hyperspectral images (HSI) over the past ten years. In SU, utilizing the spatial-contextual information allows for more realistic abundance estimation. To make full use of the spatial-spectral information, in this letter, we propose a pointwise mutual information (PMI) based graph Laplacian regularization for SU. Specifically, we construct the affinity matrices via PMI by modeling the association between neighboring image features through a statistical framework, and then we use them in the graph Laplacian regularizer. We also adopt a double reweighted $\ell_{1}$ norm minimization scheme to promote the sparsity of fractional abundances. Experimental results on simulated and real data sets prove the effectiveness of the proposed method and its superiority over competing algorithms in the literature.

Optimal graph edge weights driven nlms with multi-layer residual compensation

Non-local Means (NLMs) play essential roles in image denoising, restoration, inpainting, etc., due to its simple theory but effective performance. However, when the noise increases, the denoising accuracy of NLMs decreases significantly. This paper further develop the NLMs-based denoising method to remove noise with less loss of image details. It is realized by embedding an optimal graph edge weights driven NLMs kernel into a multi-layer residual compensation framework. Unlike the patch similarity-based weights in the traditional NLMs filters, the edge weights derived from the optimal graph Laplacian regularization consider (1) the distance between the target pixel and the candidate pixel, (2) the local gradient and (3) the patch similarity. After defining the weights, the graph-based NLMs kernel is then put into a multi-layer framework. The corresponding primal and residual terms at each layer are finally fused with learned weights to recover the image. Experimental results show that our method is effective and robust, especially for piecewise smooth images.

Optimal Graph Edge Weights Driven NLMs with Multi-layer Residual Compensation

Non-Local Means (NLMs) play important roles in image denoising, restoration, inpainting etc. due to its simple theory but effective performance. In this paper, in order to better remove noise without loss of image details, we further develop the NLMs based denoising method. It is realized by introducing a graph Laplacian regularization based weighting model and a multi-layer residual compensation strategy. Unlike the patch similarity based weights in classic NLMs filters, the graph Laplacian regularization defines the weights by considering 1) the distance between target pixel and the candidate pixel, 2) the local gradient and 3) the patch similarity. The proposed NLMs filter performs in a multi-layer framework to better remove the noise and smooth the result. The corresponding residuals at each layer are finally combined with the smooth image with learned weights to recover the image details. Experimental results show that our method is effective and robust, especially for piecewise-smooth images.