Low-Rank Matrix Recovery from Noisy via an MDL Framework-based Atomic Norm

The recovery of the underlying low-rank structure of clean data corrupted with sparse noise/outliers is attracting increasing interest. However, in many low-level vision problems, the exact target rank of the underlying structure, the particular locations and values of the sparse outliers are not known. Thus, the conventional methods can not separate the low-rank and sparse components completely, especially gross outliers or deficient observations. Therefore, in this study, we employ the Minimum Description Length (MDL) principle and atomic norm for low-rank matrix recovery to overcome these limitations. First, we employ the atomic norm to find all the candidate atoms of low-rank and sparse terms, and then we minimize the description length of the model in order to select the appropriate atoms of low-rank and the sparse matrix, respectively. Our experimental analyses show that the proposed approach can obtain a higher success rate than the state-of-the-art methods even when the number of observations is limited or the corruption ratio is high. Experimental results about synthetic data and real sensing applications (high dynamic range imaging, background modeling, removing shadows and specularities) demonstrate the effectiveness, robustness and efficiency of the proposed method.

Learning a Deep Part-based Representation by Preserving Data Distribution

Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low dimensional part-based representation of data. On the other hand, the inherent structure of the each data cluster can be described by the distribution of the intraclass samples. Then one hopes to learn a new low dimensional representation which can preserve the intrinsic structure embedded in the original high dimensional data space perfectly. In this paper, by preserving the data distribution, a deep part-based representation can be learned, and the novel algorithm is called Distribution Preserving Network Embedding (DPNE). In DPNE, we first need to estimate the distribution of the original high dimensional data using the $k$-nearest neighbor kernel density estimation, and then we seek a part-based representation which respects the above distribution. The experimental results on the real-world data sets show that the proposed algorithm has good performance in terms of cluster accuracy and AMI. It turns out that the manifold structure in the raw data can be well preserved in the low dimensional feature space.

A Multiscale Image Denoising Algorithm Based On Dilated Residual Convolution Network

Image denoising is a classical problem in low level computer vision. Model-based optimization methods and deep learning approaches have been the two main strategies for solving the problem. Model-based optimization methods are flexible for handling different inverse problems but are usually time-consuming. In contrast, deep learning methods have fast testing speed but the performance of these CNNs is still inferior. To address this issue, here we propose a novel deep residual learning model that combines the dilated residual convolution and multi-scale convolution groups. Due to the complex patterns and structures of inside an image, the multiscale convolution group is utilized to learn those patterns and enlarge the receptive field. Specifically, the residual connection and batch normalization are utilized to speed up the training process and maintain the denoising performance. In order to decrease the gridding artifacts, we integrate the hybrid dilated convolution design into our model. To this end, this paper aims to train a lightweight and effective denoiser based on multiscale convolution group. Experimental results have demonstrated that the enhanced denoiser can not only achieve promising denoising results, but also become a strong competitor in practical application.