Low rank matrix approximation (LRMA), which aims to recover the underlying low rank matrix from its degraded observation, has a wide range of applications in computer vision. The latest LRMA methods resort to using the nuclear norm minimization (NNM) as a convex relaxation of the nonconvex rank minimization. However, NNM tends to over-shrink the rank components and treats the different rank components equally, limiting its flexibility in practical applications. We propose a more flexible model, namely, the weighted Schatten p-norm minimization (WSNM), to generalize the NNM to the Schatten p-norm minimization with weights assigned to different singular values. The proposed WSNM not only gives better approximation to the original low-rank assumption, but also considers the importance of different rank components. We analyze the solution of WSNM and prove that, under certain weights permutation, WSNM can be equivalently transformed into independent non-convex lp-norm subproblems, whose global optimum can be efficiently solved by generalized iterated shrinkage algorithm. We apply WSNM to typical low-level vision problems, e.g., image denoising and background subtraction. Extensive experimental results show, both qualitatively and quantitatively, that the proposed WSNM can more effectively remove noise, and model the complex and dynamic scenes compared with state-of-the-art methods.

Image denoising is a well explored topic in the field of image processing. In the past several decades, the progress made in image denoising has benefited from the improved modeling of natural images. In this paper, we introduce a new taxonomy based on image representations for a better understanding of state-of-the-art image denoising techniques. Within each category, several representative algorithms are selected for evaluation and comparison. The experimental results are discussed and analyzed to determine the overall advantages and disadvantages of each category. In general, the nonlocal methods within each category produce better denoising results than local ones. In addition, methods based on overcomplete representations using learned dictionaries perform better than others. The comprehensive study in this paper would serve as a good reference and stimulate new research ideas in image denoising.

Exploiting the sparsity within representation models for images is critical for image denoising. The best currently available denoising methods take advantage of the sparsity from image self-similarity, pre-learned, and fixed representations. Most of these methods, however, still have difficulties in tackling high noise levels or noise models other than Gaussian. In this paper, the multiresolution structure and sparsity of wavelets are employed by nonlocal dictionary learning in each decomposition level of the wavelets. Experimental results show that our proposed method outperforms two state-of-the-art image denoising algorithms on higher noise levels. Furthermore, our approach is more adaptive to the less extensively researched uniform noise.

Electroencephalography (EEG)-based affective computing has a scarcity problem. As a result, it is difficult to build effective, highly accurate and stable models using machine learning algorithms, especially deep learning models. Data augmentation has recently shown performance improvements in deep learning models with increased accuracy, stability and reduced overfitting. In this paper, we propose a novel data augmentation framework, named the generative adversarial network-based self-supervised data augmentation (GANSER). As the first to combine adversarial training with self-supervised learning for EEG-based emotion recognition, the proposed framework generates high-quality and high-diversity simulated EEG samples. In particular, we utilize adversarial training to learn an EEG generator and force the generated EEG signals to approximate the distribution of real samples, ensuring the quality of the augmented samples. A transformation operation is employed to mask parts of the EEG signals and force the generator to synthesize potential EEG signals based on the unmasked parts to produce a wide variety of samples. A masking possibility during transformation is introduced as prior knowledge to generalize the classifier for the augmented sample space. Finally, numerous experiments demonstrate that our proposed method can improve emotion recognition with an increase in performance and achieve state-of-the-art results.