Joint Learning of Full-structure Noise in Hierarchical Bayesian Regression Models

We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing accuracy of source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where across-sensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and fully-structured. Our method has applications in many domains beyond biomagnetic inverse problems.

A Novel Multi-Modality Image Simultaneous Denoising and Fusion Method Based on Sparse Representation

Multi-modality image fusion applied to improve image quality has drawn great attention from researchers in recent years. However, noise is actually generated in images captured by different types of imaging sensors, which can seriously affect the performance of multi-modality image fusion. As the fundamental method of noisy image fusion, source images are denoised first, and then the denoised images are fused. However, image denoising can decrease the sharpness of source images to affect the fusion performance. Additionally, denoising and fusion are processed in separate processing modes, which causes an increase in computation cost. To fuse noisy multi-modality image pairs accurately and efficiently, a multi-modality image simultaneous fusion and denoising method is proposed. In the proposed method, noisy source images are decomposed into cartoon and texture components. Cartoon-texture decomposition not only decomposes source images into detail and structure components for different image fusion schemes, but also isolates image noise from texture components. A Gaussian scale mixture (GSM) based sparse representation model is presented for the denoising and fusion of texture components. A spatial domain fusion rule is applied to cartoon components. The comparative experimental results confirm the proposed simultaneous image denoising and fusion method is superior to the state-of-the-art methods in terms of visual and quantitative evaluations.

Spatial-Temporal Gaussian Scale Mixture Modeling for Foreground Estimation

Subtracting the backgrounds from the video frames is an important step for many video analysis applications. Assuming that the backgrounds are low-rank and the foregrounds are sparse, the robust principle component analysis (RPCA)-based methods have shown promising results. However, the RPCA-based methods suffered from the scale issue, i.e., the ℓ1-sparsity regularizer fails to model the varying sparsity of the moving objects. While several efforts have been made to address this issue with advanced sparse models, previous methods cannot fully exploit the spatial-temporal correlations among the foregrounds. In this paper, we proposed a novel spatial-temporal Gaussian scale mixture (STGSM) model for foreground estimation. In the proposed STGSM model, a temporal consistent constraint is imposed over the estimated foregrounds through nonzero-means Gaussian models. Specifically, the estimates of the foregrounds obtained in the previous frame are used as the prior for these of the current frame, and nonzero means Gaussian scale mixture models (GSM) are developed. To better characterize the temporal correlations, the optical flow has been used to model the correspondences between foreground pixels in adjacent frames. The spatial correlations have also been exploited by considering that local correlated pixels should be characterized by the same STGSM model, leading to further performance improvements. Experimental results on real video datasets show that the proposed method performs comparably or even better than current state-of-the-art background subtraction methods.

A Full-Reference Image Quality Assessment for Multiply Distorted Image based on Visual Mutual Information

A full-reference image quality assessment (FR-IQA) method for multi-distortion based on visual mutual information (MD-IQA) is proposed to solve the problem that the existing FR-IQA methods are mostly applicable to single-distorted images, but the assessment result for multiply distorted images is not ideal. First, the reference image and the distorted image are preprocessed by steerable pyramid decomposition and contrast sensitivity function (CSF). Next, a Gaussian scale mixture (GSM) model and an image distorted model are respectively constructed for the reference images and the distorted images. Then, visual distorted models are constructed both for the reference images and the distorted images. Finally, the mutual information between the processed reference image and the distorted image is calculated to obtain the full-reference quality assessment index for multiply distorted images. The experimental results show that the proposed method has higher accuracy and better performance for multiply distorted images.