Fengyuan Zhu

An Efficient Statistical Method for Image Noise Level Estimation

In this paper, we address the problem of estimating noise level from a single image contaminated by additive zero-mean Gaussian noise. We first provide rigorous analysis on the statistical relationship between the noise variance and the eigenvalues of the covariance matrix of patches within an image, which shows that many state-of-the-art noise estimation methods underestimate the noise level of an image. To this end, we derive a new nonparametric algorithm for efficient noise level estimation based on the observation that patches decomposed from a clean image often lie around a low-dimensional subspace. The performance of our method has been guaranteed both theoretically and empirically. Specifically, our method outperforms existing state-of-the-art algorithms on estimating noise level with the least executing time in our experiments. We further demonstrate that the denoising algorithm BM3D algorithm achieves optimal performance using noise variance estimated by our algorithm.

From Noise Modeling to Blind Image Denoising

Traditional image denoising algorithms always assume the noise to be homogeneous white Gaussian distributed. However, the noise on real images can be much more complex empirically. This paper addresses this problem and proposes a novel blind image denoising algorithm which can cope with real-world noisy images even when the noise model is not provided. It is realized by modeling image noise with mixture of Gaussian distribution (MoG) which can approximate large varieties of continuous distributions. As the number of components for MoG is unknown practically, this work adopts Bayesian nonparametric technique and proposes a novel Low-rank MoG filter (LR-MoG) to recover clean signals (patches) from noisy ones contaminated by MoG noise. Based on LR-MoG, a novel blind image denoising approach is developed. To test the proposed method, this study conducts extensive experiments on synthesis and real images. Our method achieves the state-of the-art performance consistently.

Multiclass support matrix machine for single trial EEG classification

Abstract We propose a novel multiclass classifier for single trial electroencephalogram (EEG) data in matrix form, namely multiclass support matrix machine (MSMM), aiming at improving the classification accuracy of multiclass EEG signals, and hence enhancing the performance of EEG-based brain computer interfaces (BCIs) involving multiple mental activities. In order to construct the MSMM, we propose a novel objective function, which is composed of a multiclass hinge loss term and a combined regularization term. We first formulate the multiclass hinge loss by extending the margin rescaling loss to support matrix-form data. We then devise the regularization term by combining the squared Frobenius norm of tensor-form model parameter and the nuclear norm of matrix-form hyperplanes extracted from the model parameter. While the Frobenius norm prevents over-fitting when training the model, the nuclear norm captures the structural information within the matrix data. We further propose an efficient solver for MSMM based on the alternating direction method of multipliers (ADMM) framework. We conduct extensive experiments on two benchmark EEG datasets. Experimental results show that MSMM achieves much better performance than state-of-the-art classifiers and yields a mean kappa value of 0.880 and 0.648 for dataset IIIa of BCI III and dataset IIa of BCI IV, respectively. To our best knowledge, MSMM is the first classifier that supports multiclass classification for matrix-form EEG data. The proposed MSMM enables easier and more efficient implementation of robust multi-task BCIs, and therefore has potential to promote the wider use of BCI technology.

Blind Image Denoising via Dependent Dirichlet Process Tree

Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This paper addresses this problem and proposes a novel blind image denoising algorithm to recover the clean image from noisy one with the unknown noise model. To model the empirical noise of an image, our method introduces the mixture of Gaussian distribution, which is flexible enough to approximate different continuous distributions. The problem of blind image denoising is reformulated as a learning problem. The procedure is to first build a two-layer structural model for noisy patches and consider the clean ones as latent variable. To control the complexity of the noisy patch model, this work proposes a novel Bayesian nonparametric prior called “Dependent Dirichlet Process Tree” to build the model. Then, this study derives a variational inference algorithm to estimate model parameters and recover clean patches. We apply our method on synthesis and real noisy images with different noise models. Comparing with previous approaches, ours achieves better performance. The experimental results indicate the efficiency of the proposed algorithm to cope with practical image denoising tasks.

Large-Scale Bayesian Probabilistic Matrix Factorization with Memo-Free Distributed Variational Inference

Bayesian Probabilistic Matrix Factorization (BPMF) is a powerful model in many dyadic data prediction problems, especially the applications of Recommender system. However, its poor scalability has limited its wide applications on massive data. Based on the conditional independence property of observed entries in BPMF model, we propose a novel distributed memo-free variational inference method for large-scale matrix factorization problems. Compared with the state-of-the-art methods, the proposed method is favored for several attractive properties. Specifically, it does not require tuning of learning rate carefully, shuffling the training set at each iteration, or storing massive redundant variables, and can introduce new agents into the computations on the fly. We conduct extensive experiments on both synthetic and real-world datasets. The experimental results show that our method can converge significantly faster with better prediction performance than alternative algorithms.

A Bayesian Nonparametric Approach to Dynamic Dyadic Data Prediction

An important issue of using matrix factorization for recommender systems is to capture the dynamics of user preference over time for more accurate prediction. We find that considering the existence of clusters among users with respect to evolution behavior of their preference can improve performance effectively. This is especially important to commercial recommender systems, where the evolution of preference for different users is heterogeneous, and historical ratings are not enough to estimate the preference of each user individually. Based on this, we propose a novel Bayesian nonparametric method based on the Dirichlet process, to detect users sharing the same evolution behavior of their preference. For each community, we use vector autoregressive model (VAR) to capture the evolution to explore higher-order dependency on historical user preference, and incorporate this feature with a novel adaptive prior strategy. We also derive variational inference approach to infer our method. Finally, we conduct extensive empirical experiments to show the advantage of our method over state-of-the-art algorithms.

Image denoising, local factor analysis, Bayesian Ying-Yang harmony learning

Abstract A new nonlocal-filtering method LFA-BYY is proposed for image demonizing via learning a local factor analysis (LFA) model from a polluted image under processing and then denoising the image by the learned LFA model. With the help of the Bayesian Ying-Yang (BYY) harmony learning, LFA-BYY can appropriately control the dictionary complexity and learn the noise intensity from the present image under processing, while the existing state-of-the-art methods either use a pretrained dictionary or a general basis, and require an accurate noise intensity estimation provided in advance. In comparison with BM3D, K-SVD, EPLL, and Msi on the benchmark Kodak dataset and additional medical data, experiments have shown that LFA-BYY has not only obtained competitive results on images polluted by a small noise but also outperformed these competing methods when the noise intensity increases beyond a point, especially with significant improvements as the noise intensity becomes large.