Nonconvex Nonsmooth Low-Rank Minimization via Iteratively Reweighted Nuclear Norm

The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear norm based relaxed convex problem usually leads to a suboptimal solution of the original rank minimization problem. In this paper, we propose to perform a family of nonconvex surrogates of $L_0$-norm on the singular values of a matrix to approximate the rank function. This leads to a nonconvex nonsmooth minimization problem. Then we propose to solve the problem by Iteratively Reweighted Nuclear Norm (IRNN) algorithm. IRNN iteratively solves a Weighted Singular Value Thresholding (WSVT) problem, which has a closed form solution due to the special properties of the nonconvex surrogate functions. We also extend IRNN to solve the nonconvex problem with two or more blocks of variables. In theory, we prove that IRNN decreases the objective function value monotonically, and any limit point is a stationary point. Extensive experiments on both synthesized data and real images demonstrate that IRNN enhances the low-rank matrix recovery compared with state-of-the-art convex algorithms

Generalized Nonconvex Nonsmooth Low-Rank Minimization

As surrogate functions of $L_0$-norm, many nonconvex penalty functions have been proposed to enhance the sparse vector recovery. It is easy to extend these nonconvex penalty functions on singular values of a matrix to enhance low-rank matrix recovery. However, different from convex optimization, solving the nonconvex low-rank minimization problem is much more challenging than the nonconvex sparse minimization problem. We observe that all the existing nonconvex penalty functions are concave and monotonically increasing on $[0,\infty)$. Thus their gradients are decreasing functions. Based on this property, we propose an Iteratively Reweighted Nuclear Norm (IRNN) algorithm to solve the nonconvex nonsmooth low-rank minimization problem. IRNN iteratively solves a Weighted Singular Value Thresholding (WSVT) problem. By setting the weight vector as the gradient of the concave penalty function, the WSVT problem has a closed form solution. In theory, we prove that IRNN decreases the objective function value monotonically, and any limit point is a stationary point. Extensive experiments on both synthetic data and real images demonstrate that IRNN enhances the low-rank matrix recovery compared with state-of-the-art convex algorithms.Comment: IEEE International Conference on Computer Vision and Pattern Recognition, 201

On the Sample Complexity of Multichannel Frequency Estimation via Convex Optimization

The use of multichannel data in line spectral estimation (or frequency estimation) is common for improving the estimation accuracy in array processing, structural health monitoring, wireless communications, and more. Recently proposed atomic norm methods have attracted considerable attention due to their provable superiority in accuracy, flexibility and robustness compared with conventional approaches. In this paper, we analyze atomic norm minimization for multichannel frequency estimation from noiseless compressive data, showing that the sample size per channel that ensures exact estimation decreases with the increase of the number of channels under mild conditions. In particular, given $L$ channels, order $K\left(\log K\right) \left(1+\frac{1}{L}\log N\right)$ samples per channel, selected randomly from $N$ equispaced samples, suffice to ensure with high probability exact estimation of $K$ frequencies that are normalized and mutually separated by at least $\frac{4}{N}$. Numerical results are provided corroborating our analysis.Comment: 14 pages, double column, to appear in IEEE Trans. Information Theor

ADPS: Asymmetric Distillation Post-Segmentation for Image Anomaly Detection

Knowledge Distillation-based Anomaly Detection (KDAD) methods rely on the teacher-student paradigm to detect and segment anomalous regions by contrasting the unique features extracted by both networks. However, existing KDAD methods suffer from two main limitations: 1) the student network can effortlessly replicate the teacher network's representations, and 2) the features of the teacher network serve solely as a ``reference standard" and are not fully leveraged. Toward this end, we depart from the established paradigm and instead propose an innovative approach called Asymmetric Distillation Post-Segmentation (ADPS). Our ADPS employs an asymmetric distillation paradigm that takes distinct forms of the same image as the input of the teacher-student networks, driving the student network to learn discriminating representations for anomalous regions. Meanwhile, a customized Weight Mask Block (WMB) is proposed to generate a coarse anomaly localization mask that transfers the distilled knowledge acquired from the asymmetric paradigm to the teacher network. Equipped with WMB, the proposed Post-Segmentation Module (PSM) is able to effectively detect and segment abnormal regions with fine structures and clear boundaries. Experimental results demonstrate that the proposed ADPS outperforms the state-of-the-art methods in detecting and segmenting anomalies. Surprisingly, ADPS significantly improves Average Precision (AP) metric by 9% and 20% on the MVTec AD and KolektorSDD2 datasets, respectively.Comment: 11pages,9 figure

Constructing a Non-Negative Low Rank and Sparse Graph with Data-Adaptive Features

This paper aims at constructing a good graph for discovering intrinsic data structures in a semi-supervised learning setting. Firstly, we propose to build a non-negative low-rank and sparse (referred to as NNLRS) graph for the given data representation. Specifically, the weights of edges in the graph are obtained by seeking a nonnegative low-rank and sparse matrix that represents each data sample as a linear combination of others. The so-obtained NNLRS-graph can capture both the global mixture of subspaces structure (by the low rankness) and the locally linear structure (by the sparseness) of the data, hence is both generative and discriminative. Secondly, as good features are extremely important for constructing a good graph, we propose to learn the data embedding matrix and construct the graph jointly within one framework, which is termed as NNLRS with embedded features (referred to as NNLRS-EF). Extensive experiments on three publicly available datasets demonstrate that the proposed method outperforms the state-of-the-art graph construction method by a large margin for both semi-supervised classification and discriminative analysis, which verifies the effectiveness of our proposed method

Image-Specific Information Suppression and Implicit Local Alignment for Text-based Person Search

Text-based person search (TBPS) is a challenging task that aims to search pedestrian images with the same identity from an image gallery given a query text. In recent years, TBPS has made remarkable progress and state-of-the-art methods achieve superior performance by learning local fine-grained correspondence between images and texts. However, most existing methods rely on explicitly generated local parts to model fine-grained correspondence between modalities, which is unreliable due to the lack of contextual information or the potential introduction of noise. Moreover, existing methods seldom consider the information inequality problem between modalities caused by image-specific information. To address these limitations, we propose an efficient joint Multi-level Alignment Network (MANet) for TBPS, which can learn aligned image/text feature representations between modalities at multiple levels, and realize fast and effective person search. Specifically, we first design an image-specific information suppression module, which suppresses image background and environmental factors by relation-guided localization and channel attention filtration respectively. This module effectively alleviates the information inequality problem and realizes the alignment of information volume between images and texts. Secondly, we propose an implicit local alignment module to adaptively aggregate all pixel/word features of image/text to a set of modality-shared semantic topic centers and implicitly learn the local fine-grained correspondence between modalities without additional supervision and cross-modal interactions. And a global alignment is introduced as a supplement to the local perspective. The cooperation of global and local alignment modules enables better semantic alignment between modalities. Extensive experiments on multiple databases demonstrate the effectiveness and superiority of our MANet

Boosting Few-shot Fine-grained Recognition with Background Suppression and Foreground Alignment

Few-shot fine-grained recognition (FS-FGR) aims to recognize novel fine-grained categories with the help of limited available samples. Undoubtedly, this task inherits the main challenges from both few-shot learning and fine-grained recognition. First, the lack of labeled samples makes the learned model easy to overfit. Second, it also suffers from high intra-class variance and low inter-class difference in the datasets. To address this challenging task, we propose a two-stage background suppression and foreground alignment framework, which is composed of a background activation suppression (BAS) module, a foreground object alignment (FOA) module, and a local to local (L2L) similarity metric. Specifically, the BAS is introduced to generate a foreground mask for localization to weaken background disturbance and enhance dominative foreground objects. What's more, considering the lack of labeled samples, we compute the pairwise similarity of feature maps using both the raw image and the refined image. The FOA then reconstructs the feature map of each support sample according to its correction to the query ones, which addresses the problem of misalignment between support-query image pairs. To enable the proposed method to have the ability to capture subtle differences in confused samples, we present a novel L2L similarity metric to further measure the local similarity between a pair of aligned spatial features in the embedding space. Extensive experiments conducted on multiple popular fine-grained benchmarks demonstrate that our method outperforms the existing state-of-the-art by a large margin.Comment: Preprint under review in TCSVT Journa