Low-rank structure learning via nonconvex heuristic recovery

Domain Adaptation-Based Deep Learning Model for Forecasting and Diagnosis of Glaucoma Disease

The main factor causing irreversible blindness is glaucoma. Early detection greatly reduces the risk of further vision loss. To address this problem, we developed a domain adaptation-based deep learning model called Glaucoma Domain Adaptation (GDA) based on 66,742 fundus photographs collected from 3272 eyes of 1636 subjects. GDA learns domain-invariant and domain-specific representations to extract both general and specific features. We also developed a progressive weighting mechanism to accurately transfer the source domain knowledge while mitigating the transfer of negative knowledge from the source to the target domain. We employed low-rank coding for aligning the source and target distributions. We trained GDA based on three different scenarios including eyes annotated as glaucoma due to 1) optic disc abnormalities regardless of visual field abnormalities, 2) optic disc or visual field abnormalities except ones that are glaucoma due to both optic disc and visual field abnormalities at the same time, and 3) visual field abnormalities regardless of optic disc abnormalities We then evaluate the generalizability of GDA based on two independent datasets. The AUCs of GDA in forecasting glaucoma based on the first, second, and third scenarios were 0.90, 0.88, and 0.80 and the Accuracies were 0.82, 0.78, and 0.72, respectively. The AUCs of GDA in diagnosing glaucoma based on the first, second, and third scenarios were 0.98, 0.96, and 0.93 and the Accuracies were 0.93, 0.91, and 0.88, respectively. The proposed GDA model achieved high performance and generalizability for forecasting and diagnosis of glaucoma disease from fundus photographs. GDA may augment glaucoma research and clinical practice in identifying patients with glaucoma and forecasting those who may develop glaucoma thus preventing future vision loss.

Sparse Index Tracking With K-Sparsity or ϵ-Deviation Constraint via ℓ0-Norm Minimization

Sparse index tracking, as one of the passive investment strategies, is to track a benchmark financial index via constructing a portfolio with a few assets in a market index. It can be considered as parameter learning in an adaptive system, in which we periodically update the selected assets and their investment percentages based on the sliding window approach. However, many existing algorithms for sparse index tracking cannot explicitly and directly control the number of assets or the tracking error. This article formulates sparse index tracking as two constrained optimization problems and then proposes two algorithms, namely, nonnegative orthogonal matching pursuit with projected gradient descent (NNOMP-PGD) and alternating direction method of multipliers for l0 -norm (ADMM- l0 ). The NNOMP-PGD aims at minimizing the tracking error subject to the number of selected assets less than or equal to a predefined number. With the NNOMP-PGD, investors can directly and explicitly control the number of selected assets. The ADMM- l0 aims at minimizing the number of selected assets subject to the tracking error that is upper bounded by a preset threshold. It can directly and explicitly control the tracking error. The convergence of the two proposed algorithms is also presented. With our algorithms, investors can explicitly and directly control the number of selected assets or the tracking error of the resultant portfolio. In addition, numerical experiments demonstrate that the proposed algorithms outperform the existing approaches.

Structural Smoothing Low-Rank Matrix Restoration Based on Sparse Coding and Dual-Weighted Model

Group sparse coding (GSC) uses the non-local similarity of images as constraints, which can fully exploit the structure and group sparse features of images. However, it only imposes the sparsity on the group coefficients, which limits the effectiveness of reconstructing real images. Low-rank regularized group sparse coding (LR-GSC) reduces this gap by imposing low-rankness on the group sparse coefficients. However, due to the use of non-local similarity, the edges and details of the images are over-smoothed, resulting in the blocking artifact of the images. In this paper, we propose a low-rank matrix restoration model based on sparse coding and dual weighting. In addition, total variation (TV) regularization is integrated into the proposed model to maintain local structure smoothness and edge features. Finally, to solve the problem of the proposed optimization, an optimization method is developed based on the alternating direction method. Extensive experimental results show that the proposed SDWLR-GSC algorithm outperforms state-of-the-art algorithms for image restoration when the images have large and sparse noise, such as salt and pepper noise.

Learning Dual Geometric Low-Rank Structure for Semisupervised Hyperspectral Image Classification

Most of the available graph-based semisupervised hyperspectral image classification methods adopt the cluster assumption to construct a Laplacian regularizer. However, they sometimes fail due to the existence of mixed pixels whose recorded spectra are a combination of several materials. In this paper, we propose a geometric low-rank Laplacian regularized semisupervised classifier, by exploring both the global spectral geometric structure and local spatial geometric structure of hyperspectral data. A new geometric regularized Laplacian low-rank representation (GLapLRR)-based graph is developed to evaluate spectral-spatial affinity of mixed pixels. By revealing the global low-rank and local spatial structure of images via GLapLRR, the constructed graph has the characteristics of spatial-spectral geometry description, robustness, and low sparsity, from which a more accurate classification of mixed pixels can be achieved. The proposed method is experimentally evaluated on three real hyperspectral datasets, and the results show that the proposed method outperforms its counterparts, when only a small number of labeled instances are available.

Infrared Small Target Detection Based on Non-Overlapping Patch Model via l0-l1 Norm

Infrared small target detection technology has sufficient applications in many engineering fields, such as infrared early warning, infrared tracking, and infrared reconnaissance. Due to the tiny size of the infrared small target and the lack of shape and texture information, existing methods often leave residuals or miss the target. To address these issues, a novel method based on a non-overlapping patch (NOP) joint l0-l1 norm is proposed with the introduction of sparsity regularized principal component pursuit (SRPCP). The NOP model makes the patch lighter in the first place, reducing time consumption. The adoption of the l0 norm enhances the sparsity of the target, while the adoption of the l1 norm enhances the robustness of the algorithm under clutter. As a smart optimization method, SRPCP solves the NOP model fittingly and achieves stable separation of low-rank and sparse components, thereby improving detection capacity while suppressing the background efficiently. The proposed method ultimately yielded favorable detection results. Adequate experiment results demonstrate that the proposed method is competitive in terms of background suppression and true target detection with respect to state-of-the-art methods. In addition, our method also reduces the computational time.

Learning Deep Landmarks for Imbalanced Classification

We introduce a deep imbalanced learning framework called learning DEep Landmarks in laTent spAce (DELTA). Our work is inspired by the shallow imbalanced learning approaches to rebalance imbalanced samples before feeding them to train a discriminative classifier. Our DELTA advances existing works by introducing the new concept of rebalancing samples in a deeply transformed latent space, where latent points exhibit several desired properties including compactness and separability. In general, DELTA simultaneously conducts feature learning, sample rebalancing, and discriminative learning in a joint, end-to-end framework. The framework is readily integrated with other sophisticated learning concepts including latent points oversampling and ensemble learning. More importantly, DELTA offers the possibility to conduct imbalanced learning with the assistancy of structured feature extractor. We verify the effectiveness of DELTA not only on several benchmark data sets but also on more challenging real-world tasks including click-through-rate (CTR) prediction, multi-class cell type classification, and sentiment analysis with sequential inputs.

Survey on Multi-Output Learning

The aim of multi-output learning is to simultaneously predict multiple outputs given an input. It is an important learning problem for decision-making since making decisions in the real world often involves multiple complex factors and criteria. In recent times, an increasing number of research studies have focused on ways to predict multiple outputs at once. Such efforts have transpired in different forms according to the particular multi-output learning problem under study. Classic cases of multi-output learning include multi-label learning, multi-dimensional learning, multi-target regression, and others. From our survey of the topic, we were struck by a lack in studies that generalize the different forms of multi-output learning into a common framework. This article fills that gap with a comprehensive review and analysis of the multi-output learning paradigm. In particular, we characterize the four Vs of multi-output learning, i.e., volume, velocity, variety, and veracity, and the ways in which the four Vs both benefit and bring challenges to multi-output learning by taking inspiration from big data. We analyze the life cycle of output labeling, present the main mathematical definitions of multi-output learning, and examine the field's key challenges and corresponding solutions as found in the literature. Several model evaluation metrics and popular data repositories are also discussed. Last but not least, we highlight some emerging challenges with multi-output learning from the perspective of the four Vs as potential research directions worthy of further studies.

Robust Infrared Small Target Detection via Jointly Sparse Constraint of l1/2-Metric and Dual-Graph Regularization

Small target detection is a critical step in remotely infrared searching and guiding applications. However, previously proposed algorithms would exhibit performance deterioration in the presence of complex background. It is attributed to two main reasons. First, some common background interferences are difficult to eliminate effectively by using conventional sparse measure. Second, most methods only exploit the spatial information typically, but ignore the structural priors across feature space. To address these issues, this paper gives a novel model combining the spatial-feature graph regularization and l1/2-norm sparse constraint. In this model, the spatial and feature regularizations are imposed on the sparse component in the form of graph Laplacians, where the sparse component is enforced as the eigenvectors of their graph Laplacian matrices. Such an approach is to explore the geometric information in both data and feature space simultaneously. Moreover, l1/2-norm acts as a substitute of the traditional l1-norm to constrain the sparse component, further reducing the fake targets. Finally, an efficient optimization algorithm equipped with linearized alternating direction method with adaptive penalty (LADMAP) is carefully designed for model solution. Comprehensive experiments on different infrared scenes substantiate the superiority of the proposed method beyond 11 competitive algorithms in subjective and objective evaluation.

Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation

Low-rank matrix estimation arises in a number of statistical and machine learning tasks. In particular, the coefficient matrix is considered to have a low-rank structure in multivariate linear regression and multivariate quantile regression. In this paper, we propose a method called penalized matrix least squares approximation (PMLSA) toward a unified yet simple low-rank matrix estimate. Specifically, PMLSA can transform many different types of low-rank matrix estimation problems into their asymptotically equivalent least-squares forms, which can be efficiently solved by a popular matrix fast iterative shrinkage-thresholding algorithm. Furthermore, we derive analytic degrees of freedom for PMLSA, with which a Bayesian information criterion (BIC)-type criterion is developed to select the tuning parameters. The estimated rank based on the BIC-type criterion is verified to be asymptotically consistent with the true rank under mild conditions. Extensive experimental studies are performed to confirm our assertion.

Rank-One Matrix Completion With Automatic Rank Estimation via L1-Norm Regularization

Completing a matrix from a small subset of its entries, i.e., matrix completion is a challenging problem arising from many real-world applications, such as machine learning and computer vision. One popular approach to solve the matrix completion problem is based on low-rank decomposition/factorization. Low-rank matrix decomposition-based methods often require a prespecified rank, which is difficult to determine in practice. In this paper, we propose a novel low-rank decomposition-based matrix completion method with automatic rank estimation. Our method is based on rank-one approximation, where a matrix is represented as a weighted summation of a set of rank-one matrices. To automatically determine the rank of an incomplete matrix, we impose L1-norm regularization on the weight vector and simultaneously minimize the reconstruction error. After obtaining the rank, we further remove the L1-norm regularizer and refine recovery results. With a correctly estimated rank, we can obtain the optimal solution under certain conditions. Experimental results on both synthetic and real-world data demonstrate that the proposed method not only has good performance in rank estimation, but also achieves better recovery accuracy than competing methods.

Learning Low-Rank Decomposition for Pan-Sharpening With Spatial-Spectral Offsets

Finding accurate injection components is the key issue in pan-sharpening methods. In this paper, a low-rank pan-sharpening (LRP) model is developed from a new perspective of offset learning. Two offsets are defined to represent the spatial and spectral differences between low-resolution multispectral and high-resolution multispectral (HRMS) images, respectively. In order to reduce spatial and spectral distortions, spatial equalization and spectral proportion constraints are designed and cast on the offsets, to develop a spatial and spectral constrained stable low-rank decomposition algorithm via augmented Lagrange multiplier. By fine modeling and heuristic learning, our method can simultaneously reduce spatial and spectral distortions in the fused HRMS images. Moreover, our method can efficiently deal with noises and outliers in source images, for exploring low-rank and sparse characteristics of data. Extensive experiments are taken on several image data sets, and the results demonstrate the efficiency of the proposed LRP.

Reweighted Low-Rank Matrix Analysis With Structural Smoothness for Image Denoising

In this paper, we develop a new low-rank matrix recovery algorithm for image denoising. We incorporate the total variation (TV) norm and the pixel range constraint into the existing reweighted low-rank matrix analysis to achieve structural smoothness and to significantly improve quality in the recovered image. Our proposed mathematical formulation of the low-rank matrix recovery problem combines the nuclear norm, TV norm, and norm, thereby allowing us to exploit the low-rank property of natural images, enhance the structural smoothness, and detect and remove large sparse noise. Using the iterative alternating direction and fast gradient projection methods, we develop an algorithm to solve the proposed challenging non-convex optimization problem. We conduct extensive performance evaluations on single-image denoising, hyper-spectral image denoising, and video background modeling from corrupted images. Our experimental results demonstrate that the proposed method outperforms the state-of-the-art low-rank matrix recovery methods, particularly for large random noise. For example, when the density of random sparse noise is 30%, for single-image denoising, our proposed method is able to improve the quality of the restored image by up to 4.21 dB over existing methods.

A Review of Co-Saliency Detection Algorithms

Co-saliency detection is a newly emerging and rapidly growing research area in the computer vision community. As a novel branch of visual saliency, co-saliency detection refers to the discovery of common and salient foregrounds from two or more relevant images, and it can be widely used in many computer vision tasks. The existing co-saliency detection algorithms mainly consist of three components: extracting effective features to represent the image regions, exploring the informative cues or factors to characterize co-saliency, and designing effective computational frameworks to formulate co-saliency. Although numerous methods have been developed, the literature is still lacking a deep review and evaluation of co-saliency detection techniques. In this article, we aim at providing a comprehensive review of the fundamentals, challenges, and applications of co-saliency detection. Specifically, we provide an overview of some related computer vision works, review the history of co-saliency detection, summarize and categorize the major algorithms in this research area, discuss some open issues in this area, present the potential applications of co-saliency detection, and finally point out some unsolved challenges and promising future works. We expect this review to be beneficial to both fresh and senior researchers in this field and to give insights to researchers in other related areas regarding the utility of co-saliency detection algorithms.

Information transduction capacity reduces the uncertainties in annotation-free isoform discovery and quantification

The automated transcript discovery and quantification of high-throughput RNA sequencing (RNA-seq) data are important tasks of next-generation sequencing (NGS) research. However, these tasks are challenging due to the uncertainties that arise in the inference of complete splicing isoform variants from partially observed short reads. Here, we address this problem by explicitly reducing the inherent uncertainties in a biological system caused by missing information. In our approach, the RNA-seq procedure for transforming transcripts into short reads is considered an information transmission process. Consequently, the data uncertainties are substantially reduced by exploiting the information transduction capacity of information theory. The experimental results obtained from the analyses of simulated datasets and RNA-seq datasets from cell lines and tissues demonstrate the advantages of our method over state-of-the-art competitors. Our algorithm is an open-source implementation of MaxInfo.

Descriptor Learning via Supervised Manifold Regularization for Multioutput Regression

Multioutput regression has recently shown great ability to solve challenging problems in both computer vision and medical image analysis. However, due to the huge image variability and ambiguity, it is fundamentally challenging to handle the highly complex input-target relationship of multioutput regression, especially with indiscriminate high-dimensional representations. In this paper, we propose a novel supervised descriptor learning (SDL) algorithm for multioutput regression, which can establish discriminative and compact feature representations to improve the multivariate estimation performance. The SDL is formulated as generalized low-rank approximations of matrices with a supervised manifold regularization. The SDL is able to simultaneously extract discriminative features closely related to multivariate targets and remove irrelevant and redundant information by transforming raw features into a new low-dimensional space aligned to targets. The achieved discriminative while compact descriptor largely reduces the variability and ambiguity for multioutput regression, which enables more accurate and efficient multivariate estimation. We conduct extensive evaluation of the proposed SDL on both synthetic data and real-world multioutput regression tasks for both computer vision and medical image analysis. Experimental results have shown that the proposed SDL can achieve high multivariate estimation accuracy on all tasks and largely outperforms the algorithms in the state of the arts. Our method establishes a novel SDL framework for multioutput regression, which can be widely used to boost the performance in different applications.

Discriminant Kernel Assignment for Image Coding

This paper proposes discriminant kernel assignment (DKA) in the bag-of-features framework for image representation. DKA slightly modifies existing kernel assignment to learn width-variant Gaussian kernel functions to perform discriminant local feature assignment. When directly applying gradient-descent method to solve DKA, the optimization may contain multiple time-consuming reassignment implementations in iterations. Accordingly, we introduce a more practical way to locally linearize the DKA objective and the difficult task is cast as a sequence of easier ones. Since DKA only focuses on the feature assignment part, it seamlessly collaborates with other discriminative learning approaches, e.g., discriminant dictionary learning or multiple kernel learning, for even better performances. Experimental evaluations on multiple benchmark datasets verify that DKA outperforms other image assignment approaches and exhibits significant efficiency in feature coding.

Deep Direct Reinforcement Learning for Financial Signal Representation and Trading

Can we train the computer to beat experienced traders for financial assert trading? In this paper, we try to address this challenge by introducing a recurrent deep neural network (NN) for real-time financial signal representation and trading. Our model is inspired by two biological-related learning concepts of deep learning (DL) and reinforcement learning (RL). In the framework, the DL part automatically senses the dynamic market condition for informative feature learning. Then, the RL module interacts with deep representations and makes trading decisions to accumulate the ultimate rewards in an unknown environment. The learning system is implemented in a complex NN that exhibits both the deep and recurrent structures. Hence, we propose a task-aware backpropagation through time method to cope with the gradient vanishing issue in deep training. The robustness of the neural system is verified on both the stock and the commodity future markets under broad testing conditions.

Multi-stage classification method oriented to aerial image based on low-rank recovery and multi-feature fusion sparse representation

Automatic classification of terrain surfaces from an aerial image is essential for an autonomous unmanned aerial vehicle (UAV) landing at an unprepared site by using vision. Diverse terrain surfaces may show similar spectral properties due to the illumination and noise that easily cause poor classification performance. To address this issue, a multi-stage classification algorithm based on low-rank recovery and multi-feature fusion sparse representation is proposed. First, color moments and Gabor texture feature are extracted from training data and stacked as column vectors of a dictionary. Then we perform low-rank matrix recovery for the dictionary by using augmented Lagrange multipliers and construct a multi-stage terrain classifier. Experimental results on an aerial map database that we prepared verify the classification accuracy and robustness of the proposed method.

Learning Robust and Discriminative Subspace With Low-Rank Constraints

In this paper, we aim at learning robust and discriminative subspaces from noisy data. Subspace learning is widely used in extracting discriminative features for classification. However, when data are contaminated with severe noise, the performance of most existing subspace learning methods would be limited. Recent advances in low-rank modeling provide effective solutions for removing noise or outliers contained in sample sets, which motivates us to take advantage of low-rank constraints in order to exploit robust and discriminative subspace for classification. In particular, we present a discriminative subspace learning method called the supervised regularization-based robust subspace (SRRS) approach, by incorporating the low-rank constraint. SRRS seeks low-rank representations from the noisy data, and learns a discriminative subspace from the recovered clean data jointly. A supervised regularization function is designed to make use of the class label information, and therefore to enhance the discriminability of subspace. Our approach is formulated as a constrained rank-minimization problem. We design an inexact augmented Lagrange multiplier optimization algorithm to solve it. Unlike the existing sparse representation and low-rank learning methods, our approach learns a low-dimensional subspace from recovered data, and explicitly incorporates the supervised information. Our approach and some baselines are evaluated on the COIL-100, ALOI, Extended YaleB, FERET, AR, and KinFace databases. The experimental results demonstrate the effectiveness of our approach, especially when the data contain considerable noise or variations.

Tensor LRR and Sparse Coding-Based Subspace Clustering

Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows exponentially with the number of dimensions. To address these issues, we propose a tensor low-rank representation (TLRR) and sparse coding-based (TLRRSC) subspace clustering method by simultaneously considering feature information and spatial structures. TLRR seeks the lowest rank representation over original spatial structures along all spatial directions. Sparse coding learns a dictionary along feature spaces, so that each sample can be represented by a few atoms of the learned dictionary. The affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. TLRRSC can well capture the global structure and inherent feature information of data and provide a robust subspace segmentation from corrupted data. Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established stateof- the-art methods.

Deep and Structured Robust Information Theoretic Learning for Image Analysis

This paper presents a robust information theoretic (RIT) model to reduce the uncertainties, i.e., missing and noisy labels, in general discriminative data representation tasks. The fundamental pursuit of our model is to simultaneously learn a transformation function and a discriminative classifier that maximize the mutual information of data and their labels in the latent space. In this general paradigm, we, respectively, discuss three types of the RIT implementations with linear subspace embedding, deep transformation, and structured sparse learning. In practice, the RIT and deep RIT are exploited to solve the image categorization task whose performances will be verified on various benchmark data sets. The structured sparse RIT is further applied to a medical image analysis task for brain magnetic resonance image segmentation that allows group-level feature selections on the brain tissues.

PHOCOS: inferring multi-feature phenotypic crosstalk networks

Motivation: Quantification of cellular changes to perturbations can provide a powerful approach to infer crosstalk among molecular components in biological networks. Existing crosstalk inference methods conduct network-structure learning based on a single phenotypic feature (e.g. abundance) of a biomarker. These approaches are insufficient for analyzing perturbation data that can contain information about multiple features (e.g. abundance, activity or localization) of each biomarker.

Results: We propose a computational framework for inferring phenotypic crosstalk (PHOCOS) that is suitable for high-content microscopy or other modalities that capture multiple phenotypes per biomarker. PHOCOS uses a robust graph-learning paradigm to predict direct effects from potential indirect effects and identify errors owing to noise or missing links. The result is a multi-feature, sparse network that parsimoniously captures direct and strong interactions across phenotypic attributes of multiple biomarkers. We use simulated and biological data to demonstrate the ability of PHOCOS to recover multi-attribute crosstalk networks from cellular perturbation assays.

Availability and implementation: PHOCOS is available in open source at https://github.com/AltschulerWu-Lab/PHOCOS

Contact:steven.altschuler@ucsf.edu or lani.wu@ucsf.edu

Integrated Low-Rank-Based Discriminative Feature Learning for Recognition

Feature learning plays a central role in pattern recognition. In recent years, many representation-based feature learning methods have been proposed and have achieved great success in many applications. However, these methods perform feature learning and subsequent classification in two separate steps, which may not be optimal for recognition tasks. In this paper, we present a supervised low-rank-based approach for learning discriminative features. By integrating latent low-rank representation (LatLRR) with a ridge regression-based classifier, our approach combines feature learning with classification, so that the regulated classification error is minimized. In this way, the extracted features are more discriminative for the recognition tasks. Our approach benefits from a recent discovery on the closed-form solutions to noiseless LatLRR. When there is noise, a robust Principal Component Analysis (PCA)-based denoising step can be added as preprocessing. When the scale of a problem is large, we utilize a fast randomized algorithm to speed up the computation of robust PCA. Extensive experimental results demonstrate the effectiveness and robustness of our method.

DC Proximal Newton for Nonconvex Optimization Problems

We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are nonconvex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal Newton algorithm that is able to deal with such a situation. The algorithm consists in obtaining a descent direction from an approximation of the loss function and then in performing a line search to ensure a sufficient descent. A theoretical analysis is provided showing that the iterates of the proposed algorithm admit as limit points stationary points of the DC objective function. Numerical experiments show that our approach is more efficient than the current state of the art for a problem with a convex loss function and a nonconvex regularizer. We have also illustrated the benefit of our algorithm in high-dimensional transductive learning problem where both the loss function and regularizers are nonconvex.

Noise reduction of diffusion tensor images by sparse representation and dictionary learning

Background

The low quality of diffusion tensor image (DTI) could affect the accuracy of oncology diagnosis.

Methods

We present a novel sparse representation based denoising method for three dimensional DTI by learning adaptive dictionary with the context redundancy between neighbor slices. In this study, the context redundancy among the adjacent slices of the diffusion weighted imaging volumes is utilized to train sparsifying dictionaries. Therefore, higher redundancy could be achieved for better description of image with lower computation complexity. The optimization problem is solved efficiently using an iterative block-coordinate relaxation method.

Results

The effectiveness of our proposed method has been assessed on both simulated and real experimental DTI datasets. Qualitative and quantitative evaluations demonstrate the performance of the proposed method on the simulated data. The experiments on real datasets with different b-values also show the effectiveness of the proposed method for noise reduction of DTI.

Conclusions

The proposed approach well removes the noise in the DTI, which has high potential to be applied for clinical oncology applications.

Shape-Constrained Sparse and Low-Rank Decomposition for Auroral Substorm Detection

An auroral substorm is an important geophysical phenomenon that reflects the interaction between the solar wind and the Earth's magnetosphere. Detecting substorms is of practical significance in order to prevent disruption to communication and global positioning systems. However, existing detection methods can be inaccurate or require time-consuming manual analysis and are therefore impractical for large-scale data sets. In this paper, we propose an automatic auroral substorm detection method based on a shape-constrained sparse and low-rank decomposition (SCSLD) framework. Our method automatically detects real substorm onsets in large-scale aurora sequences, which overcomes the limitations of manual detection. To reduce noise interference inherent in current SLD methods, we introduce a shape constraint to force the noise to be assigned to the low-rank part (stationary background), thus ensuring the accuracy of the sparse part (moving object) and improving the performance. Experiments conducted on aurora sequences in solar cycle 23 (1996-2008) show that the proposed SCSLD method achieves good performance for motion analysis of aurora sequences. Moreover, the obtained results are highly consistent with manual analysis, suggesting that the proposed automatic method is useful and effective in practice.

MRM-Lasso: A Sparse Multiview Feature Selection Method via Low-Rank Analysis

Learning about multiview data involves many applications, such as video understanding, image classification, and social media. However, when the data dimension increases dramatically, it is important but very challenging to remove redundant features in multiview feature selection. In this paper, we propose a novel feature selection algorithm, multiview rank minimization-based Lasso (MRM-Lasso), which jointly utilizes Lasso for sparse feature selection and rank minimization for learning relevant patterns across views. Instead of simply integrating multiple Lasso from view level, we focus on the performance of sample-level (sample significance) and introduce pattern-specific weights into MRM-Lasso. The weights are utilized to measure the contribution of each sample to the labels in the current view. In addition, the latent correlation across different views is successfully captured by learning a low-rank matrix consisting of pattern-specific weights. The alternating direction method of multipliers is applied to optimize the proposed MRM-Lasso. Experiments on four real-life data sets show that features selected by MRM-Lasso have better multiview classification performance than the baselines. Moreover, pattern-specific weights are demonstrated to be significant for learning about multiview data, compared with view-specific weights.

Automatic face naming by learning discriminative affinity matrices from weakly labeled images

Given a collection of images, where each image contains several faces and is associated with a few names in the corresponding caption, the goal of face naming is to infer the correct name for each face. In this paper, we propose two new methods to effectively solve this problem by learning two discriminative affinity matrices from these weakly labeled images. We first propose a new method called regularized low-rank representation by effectively utilizing weakly supervised information to learn a low-rank reconstruction coefficient matrix while exploring multiple subspace structures of the data. Specifically, by introducing a specially designed regularizer to the low-rank representation method, we penalize the corresponding reconstruction coefficients related to the situations where a face is reconstructed by using face images from other subjects or by using itself. With the inferred reconstruction coefficient matrix, a discriminative affinity matrix can be obtained. Moreover, we also develop a new distance metric learning method called ambiguously supervised structural metric learning by using weakly supervised information to seek a discriminative distance metric. Hence, another discriminative affinity matrix can be obtained using the similarity matrix (i.e., the kernel matrix) based on the Mahalanobis distances of the data. Observing that these two affinity matrices contain complementary information, we further combine them to obtain a fused affinity matrix, based on which we develop a new iterative scheme to infer the name of each face. Comprehensive experiments demonstrate the effectiveness of our approach.

Robust Exemplar Extraction Using Structured Sparse Coding

Robust exemplar extraction from the noisy sample set is one of the most important problems in pattern recognition. In this brief, we propose a novel approach for exemplar extraction through structured sparse learning. The new model accounts for not only the reconstruction capability and the sparsity, but also the diversity and robustness. To solve the optimization problem, we adopt the alternating directional method of multiplier technology to design an iterative algorithm. Finally, the effectiveness of the approach is demonstrated by experiments of various examples including traffic sign sequences.

Logsum using Garbled Circuits

Secure multiparty computation allows for a set of users to evaluate a particular function over their inputs without revealing the information they possess to each other. Theoretically, this can be achieved using fully homomorphic encryption systems, but so far they remain in the realm of computational impracticability. An alternative is to consider secure function evaluation using homomorphic public-key cryptosystems or Garbled Circuits, the latter being a popular trend in recent times due to important breakthroughs. We propose a technique for computing the logsum operation using Garbled Circuits. This technique relies on replacing the logsum operation with an equivalent piecewise linear approximation, taking advantage of recent advances in efficient methods for both designing and implementing Garbled Circuits. We elaborate on how all the required blocks should be assembled in order to obtain small errors regarding the original logsum operation and very fast execution times.

Resolving transient time profile in ToF imaging via log-sum sparse regularization

Multi-frequency time-of-flight (ToF) cameras have been used to recover the transient time profiles of optical responses such that multipath interference can be separated. The resolution of the recovered time profiles is limited by the highest modulation frequency. Here, we demonstrate a method based on log-sum sparsity regularization to recover transient time profiles of specular reflections. We show that it improves the ability of separating pulses better than the state-of-the-art regularization methods. As an application, we demonstrate the encoding and decoding of hidden images using mirror reflections.

Reweighted low-rank matrix recovery and its application in image restoration

In this paper, we propose a reweighted low-rank matrix recovery method and demonstrate its application for robust image restoration. In the literature, principal component pursuit solves low-rank matrix recovery problem via a convex program of mixed nuclear norm and l1 norm. Inspired by reweighted l1 minimization for sparsity enhancement, we propose reweighting singular values to enhance low rank of a matrix. An efficient iterative reweighting scheme is proposed for enhancing low rank and sparsity simultaneously and the performance of low-rank matrix recovery is prompted greatly. We demonstrate the utility of the proposed method both on numerical simulations and real images/videos restoration, including single image restoration, hyperspectral image restoration, and background modeling from corrupted observations. All of these experiments give empirical evidence on significant improvements of the proposed algorithm over previous work on low-rank matrix recovery.

Structure-constrained low-rank representation

Benefiting from its effectiveness in subspace segmentation, low-rank representation (LRR) and its variations have many applications in computer vision and pattern recognition, such as motion segmentation, image segmentation, saliency detection, and semisupervised learning. It is known that the standard LRR can only work well under the assumption that all the subspaces are independent. However, this assumption cannot be guaranteed in real-world problems. This paper addresses this problem and provides an extension of LRR, named structure-constrained LRR (SC-LRR), to analyze the structure of multiple disjoint subspaces, which is more general for real vision data. We prove that the relationship of multiple linear disjoint subspaces can be exactly revealed by SC-LRR, with a predefined weight matrix. As a nontrivial byproduct, we also illustrate that SC-LRR can be applied for semisupervised learning. The experimental results on different types of vision problems demonstrate the effectiveness of our proposed method.

Visual words assignment via information-theoretic manifold embedding

Codebook-based learning provides a flexible way to extract the contents of an image in a data-driven manner for visual recognition. One central task in such frameworks is codeword assignment, which allocates local image descriptors to the most similar codewords in the dictionary to generate histogram for categorization. Nevertheless, existing assignment approaches, e.g., nearest neighbors strategy (hard assignment) and Gaussian similarity (soft assignment), suffer from two problems: 1) too strong Euclidean assumption and 2) neglecting the label information of the local descriptors. To address the aforementioned two challenges, we propose a graph assignment method with maximal mutual information (GAMI) regularization. GAMI takes the power of manifold structure to better reveal the relationship of massive number of local features by nonlinear graph metric. Meanwhile, the mutual information of descriptor-label pairs is ultimately optimized in the embedding space for the sake of enhancing the discriminant property of the selected codewords. According to such objective, two optimization models, i.e., inexact-GAMI and exact-GAMI, are respectively proposed in this paper. The inexact model can be efficiently solved with a closed-from solution. The stricter exact-GAMI nonparametrically estimates the entropy of descriptor-label pairs in the embedding space and thus leads to a relatively complicated but still trackable optimization. The effectiveness of GAMI models are verified on both the public and our own datasets.

Robust and accurate transient light transport decomposition via convolutional sparse coding

Ultrafast sources and detectors have been used to record the time-resolved scattering of light propagating through macroscopic scenes. In the context of computational imaging, decomposition of this transient light transport (TLT) is useful for applications, such as characterizing materials, imaging through diffuser layers, and relighting scenes dynamically. Here, we demonstrate a method of convolutional sparse coding to decompose TLT into direct reflections, inter-reflections, and subsurface scattering. The method relies on the sparsity composition of the time-resolved kernel. We show that it is robust and accurate to noise during the acquisition process.

Adaptive distance metric learning for diffusion tensor image segmentation

High quality segmentation of diffusion tensor images (DTI) is of key interest in biomedical research and clinical application. In previous studies, most efforts have been made to construct predefined metrics for different DTI segmentation tasks. These methods require adequate prior knowledge and tuning parameters. To overcome these disadvantages, we proposed to automatically learn an adaptive distance metric by a graph based semi-supervised learning model for DTI segmentation. An original discriminative distance vector was first formulated by combining both geometry and orientation distances derived from diffusion tensors. The kernel metric over the original distance and labels of all voxels were then simultaneously optimized in a graph based semi-supervised learning approach. Finally, the optimization task was efficiently solved with an iterative gradient descent method to achieve the optimal solution. With our approach, an adaptive distance metric could be available for each specific segmentation task. Experiments on synthetic and real brain DTI datasets were performed to demonstrate the effectiveness and robustness of the proposed distance metric learning approach. The performance of our approach was compared with three classical metrics in the graph based semi-supervised learning framework.

Joint non-Gaussian denoising and superresolving of raw high frame rate videos

High frame rate cameras capture sharp videos of highly dynamic scenes by trading off signal-noise-ratio and image resolution, so combinational super-resolving and denoising is crucial for enhancing high speed videos and extending their applications. The solution is nontrivial due to the fact that two deteriorations co-occur during capturing and noise is nonlinearly dependent on signal strength. To handle this problem, we propose conducting noise separation and super resolution under a unified optimization framework, which models both spatiotemporal priors of high quality videos and signal-dependent noise. Mathematically, we align the frames along temporal axis and pursue the solution under the following three criterion: 1) the sharp noise-free image stack is low rank with some missing pixels denoting occlusions; 2) the noise follows a given nonlinear noise model; and 3) the recovered sharp image can be reconstructed well with sparse coefficients and an over complete dictionary learned from high quality natural images. In computation aspects, we propose to obtain the final result by solving a convex optimization using the modern local linearization techniques. In the experiments, we validate the proposed approach in both synthetic and real captured data.

Free-viewpoint video of human actors using multiple handheld Kinects

We present an algorithm for creating free-viewpoint video of interacting humans using three handheld Kinect cameras. Our method reconstructs deforming surface geometry and temporal varying texture of humans through estimation of human poses and camera poses for every time step of the RGBZ video. Skeletal configurations and camera poses are found by solving a joint energy minimization problem, which optimizes the alignment of RGBZ data from all cameras, as well as the alignment of human shape templates to the Kinect data. The energy function is based on a combination of geometric correspondence finding, implicit scene segmentation, and correspondence finding using image features. Finally, texture recovery is achieved through jointly optimization on spatio-temporal RGB data using matrix completion. As opposed to previous methods, our algorithm succeeds on free-viewpoint video of human actors under general uncontrolled indoor scenes with potentially dynamic background, and it succeeds even if the cameras are moving.

Differences help recognition: a probabilistic interpretation

This paper presents a computational model to address one prominent psychological behavior of human beings to recognize images. The basic pursuit of our method can be concluded as that differences among multiple images help visual recognition. Generally speaking, we propose a statistical framework to distinguish what kind of image features capture sufficient category information and what kind of image features are common ones shared in multiple classes. Mathematically, the whole formulation is subject to a generative probabilistic model. Meanwhile, a discriminative functionality is incorporated into the model to interpret the differences among all kinds of images. The whole Bayesian formulation is solved in an Expectation-Maximization paradigm. After finding those discriminative patterns among different images, we design an image categorization algorithm to interpret how these differences help visual recognition within the bag-of-feature framework. The proposed method is verified on a variety of image categorization tasks including outdoor scene images, indoor scene images as well as the airborne SAR images from different perspectives.