In this paper, we aim to recover the 3D human pose from 2D body joints of a single image. The major challenge in this task is the depth ambiguity since different 3D poses may produce similar 2D poses. Although many recent advances in this problem are found in both unsupervised and supervised learning approaches, the performances of most of these approaches are greatly affected by insufficient diversities and richness of training data. To alleviate this issue, we propose an unsupervised learning approach, which is capable of estimating various complex poses well under limited available training data. Specifically, we propose a Shape Decomposition Model (SDM) in which a 3D pose is considered as the superposition of two parts which are global structure together with some deformations. Based on SDM, we estimate these two parts explicitly by solving two sets of different distributed combination coefficients of geometric priors. In addition, to obtain geometric priors, a joint dictionary learning algorithm is proposed to extract both coarse and fine pose clues simultaneously from limited training data. Quantitative evaluations on several widely used datasets demonstrate that our approach yields better performances over other competitive approaches. Especially, on some categories with more complex deformations, significant improvements are achieved by our approach. Furthermore, qualitative experiments conducted on in-the-wild images also show the effectiveness of the proposed approach.
In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $\mathbb{R}^d$), and the goal is to find a "basis" in which the signals have a sparse (approximate) representation. The problem has received a lot of attention in signal processing, learning, and theoretical computer science. The problem is formalized as factorizing a matrix $X (d \times n)$ (whose columns are the signals) as $X = AY$, where $A$ has a prescribed number $m$ of columns (typically $m \ll n$), and $Y$ has columns that are $k$-sparse (typically $k \ll d$). Most of the known theoretical results involve assuming that the columns of the unknown $A$ have certain incoherence properties, and that the coefficient matrix $Y$ has random (or partly random) structure. The goal of our work is to understand what can be said in the absence of such assumptions. Can we still find $A$ and $Y$ such that $X \approx AY$? We show that this is possible, if we allow violating the bounds on $m$ and $k$ by appropriate factors that depend on $k$ and the desired approximation. Our results rely on an algorithm for what we call the threshold correlation problem, which turns out to be related to hypercontractive norms of matrices. We also show that our algorithmic ideas apply to a setting in which some of the columns of $X$ are outliers, thus giving similar guarantees even in this challenging setting.
In this paper, we propose an analysis mechanism based structured Analysis Discriminative Dictionary Learning (ADDL) framework. ADDL seamlessly integrates the analysis discriminative dictionary learning, analysis representation and analysis classifier training into a unified model. The applied analysis mechanism can make sure that the learnt dictionaries, representations and linear classifiers over different classes are independent and discriminating as much as possible. The dictionary is obtained by minimizing a reconstruction error and an analytical incoherence promoting term that encourages the sub-dictionaries associated with different classes to be independent. To obtain the representation coefficients, ADDL imposes a sparse l2,1-norm constraint on the coding coefficients instead of using l0 or l1-norm, since the l0 or l1-norm constraint applied in most existing DL criteria makes the training phase time consuming. The codes-extraction projection that bridges data with the sparse codes by extracting special features from the given samples is calculated via minimizing a sparse codes approximation term. Then we compute a linear classifier based on the approximated sparse codes by an analysis mechanism to simultaneously consider the classification and representation powers. Thus, the classification approach of our model is very efficient, because it can avoid the extra time-consuming sparse reconstruction process with trained dictionary for each new test data as most existing DL algorithms. Simulations on real image databases demonstrate that our ADDL model can obtain superior performance over other state-of-the-arts.
We propose a novel structured discriminative block-diagonal dictionary learning method, referred to as scalable Locality-Constrained Projective Dictionary Learning (LC-PDL), for efficient representation and classification. To improve the scalability by saving both training and testing time, our LC-PDL aims at learning a structured discriminative dictionary and a block-diagonal representation without using costly l0/l1-norm. Besides, it avoids extra time-consuming sparse reconstruction process with the well-trained dictionary for new sample as many existing models. More importantly, LC-PDL avoids using the complementary data matrix to learn the sub-dictionary over each class. To enhance the performance, we incorporate a locality constraint of atoms into the DL procedures to keep local information and obtain the codes of samples over each class separately. A block-diagonal discriminative approximation term is also derived to learn a discriminative projection to bridge data with their codes by extracting the special block-diagonal features from data, which can ensure the approximate coefficients to associate with its label information clearly. Then, a robust multiclass classifier is trained over extracted block-diagonal codes for accurate label predictions. Experimental results verify the effectiveness of our algorithm.
Unsupervised Domain Adaptation (UDA) addresses the problem of performance degradation due to domain shift between training and testing sets, which is common in computer vision applications. Most existing UDA approaches are based on vector-form data although the typical format of data or features in visual applications is multi-dimensional tensor. Besides, current methods, including the deep network approaches, assume that abundant labeled source samples are provided for training. However, the number of labeled source samples are always limited due to expensive annotation cost in practice, making sub-optimal performance been observed. In this paper, we propose to seek discriminative representation for multi-dimensional data by learning a structured dictionary in tensor space. The dictionary separates domain-specific information and class-specific information to guarantee the representation robust to domains. In addition, a pseudo-label estimation scheme is developed to combine with discriminant analysis in the algorithm iteration for avoiding the external classifier design. We perform extensive results on different datasets with limited source samples. Experimental results demonstrates that the proposed method outperforms the state-of-the-art approaches.
The potential huge advantage of spectral computed tomography (CT) is its capability to provide accuracy material identification and quantitative tissue information. This can benefit clinical applications, such as brain angiography, early tumor recognition, etc. To achieve more accurate material components with higher material image quality, we develop a dictionary learning based image-domain material decomposition (DLIMD) for spectral CT in this paper. First, we reconstruct spectral CT image from projections and calculate material coefficients matrix by selecting uniform regions of basis materials from image reconstruction results. Second, we employ the direct inversion (DI) method to obtain initial material decomposition results, and a set of image patches are extracted from the mode-1 unfolding of normalized material image tensor to train a united dictionary by the K-SVD technique. Third, the trained dictionary is employed to explore the similarities from decomposed material images by constructing the DLIMD model. Fourth, more constraints (i.e., volume conservation and the bounds of each pixel within material maps) are further integrated into the model to improve the accuracy of material decomposition. Finally, both physical phantom and preclinical experiments are employed to evaluate the performance of the proposed DLIMD in material decomposition accuracy, material image edge preservation and feature recovery.
Dictionary learning methods can be split into: i) class specific dictionary learning ii) class shared dictionary learning. The difference between the two categories is how to use discriminative information. With the first category, samples of different classes are mapped into different subspaces, which leads to some redundancy with the class specific base vectors. While for the second category, the samples in each specific class can not be described accurately. In this paper, we first propose a novel class shared dictionary learning method named label embedded dictionary learning (LEDL). It is the improvement based on LCKSVD, which is easier to find out the optimal solution. Then we propose a novel framework named cascaded dictionary learning framework (CDLF) to combine the specific dictionary learning with shared dictionary learning to describe the feature to boost the performance of classification sufficiently. Extensive experimental results on six benchmark datasets illustrate that our methods are capable of achieving superior performance compared to several state-of-art classification algorithms.
We introduce a neural-network architecture, termed the constrained recurrent sparse autoencoder (CRsAE), that solves convolutional dictionary learning problems, thus establishing a link between dictionary learning and neural networks. Specifically, we leverage the interpretation of the alternating-minimization algorithm for dictionary learning as an approximate Expectation-Maximization algorithm to develop autoencoders that enable the simultaneous training of the dictionary and regularization parameter (ReLU bias). The forward pass of the encoder approximates the sufficient statistics of the E-step as the solution to a sparse coding problem, using an iterative proximal gradient algorithm called FISTA. The encoder can be interpreted either as a recurrent neural network or as a deep residual network, with two-sided ReLU non-linearities in both cases. The M-step is implemented via a two-stage back-propagation. The first stage relies on a linear decoder applied to the encoder and a norm-squared loss. It parallels the dictionary update step in dictionary learning. The second stage updates the regularization parameter by applying a loss function to the encoder that includes a prior on the parameter motivated by Bayesian statistics. We demonstrate in an image-denoising task that CRsAE learns Gabor-like filters, and that the EM-inspired approach for learning biases is superior to the conventional approach. In an application to recordings of electrical activity from the brain, we demonstrate that CRsAE learns realistic spike templates and speeds up the process of identifying spike times by 900x compared to algorithms based on convex optimization.
In this letter, we propose a novel computationally efficient coupled dictionary learning method that enforces pairwise correlation between the atoms of dictionaries learned to represent the underlying feature spaces of two different representations of the same signals, e.g., representations in different modalities or representations of the same signals measured with different qualities. The jointly learned correlated feature spaces represented by coupled dictionaries are used in sparse representation based classification, recognition and reconstruction tasks. The presented experimental results show that the proposed coupled dictionary learning method has a significantly lower computational cost. Moreover, the visual presentation of jointly learned dictionaries shows that the pairwise correlations between the corresponding atoms are ensured.
Matrix factorization (MF) is a versatile learning method that has found wide applications in various data-driven disciplines. Still, many MF algorithms do not adequately scale with the size of available datasets and/or lack interpretability. To improve the computational efficiency of the method, an online (streaming) MF algorithm was proposed in Mairal et al. [2010]. To enable data interpretability, a constrained version of MF, termed convex MF, was introduced in Ding et al. [2010]. In the latter work, the basis vectors are required to lie in the convex hull of the data samples, thereby ensuring that every basis can be interpreted as a weighted combination of data samples. No current algorithmic solutions for online convex MF are known as it is challenging to find adequate convex bases without having access to the complete dataset. We address both problems by proposing the first online convex MF algorithm that maintains a collection of constant-size sets of representative data samples needed for interpreting each of the basis (Ding et al. [2010]) and has the same almost sure convergence guarantees as the online learning algorithm of Mairal et al. [2010]. Our proof techniques combine random coordinate descent algorithms with specialized quasi-martingale convergence analysis. Experiments on synthetic and real world datasets show significant computational savings of the proposed online convex MF method compared to classical convex MF. Since the proposed method maintains small representative sets of data samples needed for convex interpretations, it is related to a body of work in theoretical computer science, pertaining to generating point sets (Blum et al. [2016]), and in computer vision, pertaining to archetypal analysis (Mei et al. [2018]). Nevertheless, it differs from these lines of work both in terms of the objective and algorithmic implementations.
In this work we reduce undersampling artefacts in two-dimensional ($2D$) golden-angle radial cine cardiac MRI by applying a modified version of the U-net. We train the network on $2D$ spatio-temporal slices which are previously extracted from the image sequences. We compare our approach to two $2D$ and a $3D$ Deep Learning-based post processing methods and to three iterative reconstruction methods for dynamic cardiac MRI. Our method outperforms the $2D$ spatially trained U-net and the $2D$ spatio-temporal U-net. Compared to the $3D$ spatio-temporal U-net, our method delivers comparable results, but with shorter training times and less training data. Compared to the Compressed Sensing-based methods $kt$-FOCUSS and a total variation regularised reconstruction approach, our method improves image quality with respect to all reported metrics. Further, it achieves competitive results when compared to an iterative reconstruction method based on adaptive regularization with Dictionary Learning and total variation, while only requiring a small fraction of the computational time. A persistent homology analysis demonstrates that the data manifold of the spatio-temporal domain has a lower complexity than the spatial domain and therefore, the learning of a projection-like mapping is facilitated. Even when trained on only one single subject without data-augmentation, our approach yields results which are similar to the ones obtained on a large training dataset. This makes the method particularly suitable for training a network on limited training data. Finally, in contrast to the spatial $2D$ U-net, our proposed method is shown to be naturally robust with respect to image rotation in image space and almost achieves rotation-equivariance where neither data-augmentation nor a particular network design are required.
There are some inadequacies in the language description of this paper that require further improvement. This paper is based on a revision of a conference paper. It is now necessary to further explain the difference between the contributions of the two papers.
This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing the separable dictionary learning model. Two different approaches for learning mixture of separable dictionaries are explored and sufficient conditions for local identifiability of the underlying dictionary are derived in each case. Moreover, computational algorithms are developed to solve the problem of learning mixture of separable dictionaries in both batch and online settings. Numerical experiments are used to show the usefulness of the proposed model and the efficacy of the developed algorithms.
Over the past few years, dictionary learning (DL)-based methods have been successfully used in various image reconstruction problems. However, traditional DL-based computed tomography (CT) reconstruction methods are patch-based and ignore the consistency of pixels in overlapped patches. In addition, the features learned by these methods always contain shifted versions of the same features. In recent years, convolutional sparse coding (CSC) has been developed to address these problems. In this paper, inspired by several successful applications of CSC in the field of signal processing, we explore the potential of CSC in sparse-view CT reconstruction. By directly working on the whole image, without the necessity of dividing the image into overlapped patches in DL-based methods, the proposed methods can maintain more details and avoid artifacts caused by patch aggregation. With predetermined filters, an alternating scheme is developed to optimize the objective function. Extensive experiments with simulated and real CT data were performed to validate the effectiveness of the proposed methods. Qualitative and quantitative results demonstrate that the proposed methods achieve better performance than several existing state-of-the-art methods.
In this paper, we propose a non-negative representation based discriminative dictionary learning algorithm (NRDL) for multicategory face classification. In contrast to traditional dictionary learning methods, NRDL investigates the use of non-negative representation (NR), which contributes to learning discriminative dictionary atoms. In order to make the learned dictionary more suitable for classification, NRDL seamlessly incorporates nonnegative representation constraint, discriminative dictionary learning and linear classifier training into a unified model. Specifically, NRDL introduces a positive constraint on representation matrix to find distinct atoms from heterogeneous training samples, which results in sparse and discriminative representation. Moreover, a discriminative dictionary encouraging function is proposed to enhance the uniqueness of class-specific sub-dictionaries. Meanwhile, an inter-class incoherence constraint and a compact graph based regularization term are constructed to respectively improve the discriminability of learned classifier. Experimental results on several benchmark face data sets verify the advantages of our NRDL algorithm over the state-of-the-art dictionary learning methods.
Age-related Macular Degeneration (AMD) and Diabetic Macular Edema (DME) are the major causes of vision loss in developed countries. Alteration of retinal layer structure and appearance of exudate are the most significant signs of these diseases. With the aim of automatic classification of DME, AMD and normal subjects from Optical Coherence Tomography (OCT) images, we proposed a classification algorithm. The two important issues intended in this approach are, not utilizing retinal layer segmentation which by itself is a challenging task and attempting to identify diseases in their early stages, where the signs of diseases appear in a small fraction of B-Scans. We used a histogram of oriented gradients (HOG) feature descriptor to well characterize the distribution of local intensity gradients and edge directions. In order to capture the structure of extracted features, we employed different dictionary learning-based classifiers. Our dataset consists of 45 subjects: 15 patients with AMD, 15 patients with DME and 15 normal subjects. The proposed classifier leads to an accuracy of 95.13%, 100.00%, and 100.00% for DME, AMD, and normal OCT images, respectively, only by considering the 4% of all B-Scans of a volume which outperforms the state of the art methods.
In recent years, kernel-based sparse coding (K-SRC) has received particular attention due to its efficient representation of nonlinear data structures in the feature space. Nevertheless, the existing K-SRC methods suffer from the lack of consistency between their training and test optimization frameworks. In this work, we propose a novel confident K-SRC and dictionary learning algorithm (CKSC) which focuses on the discriminative reconstruction of the data based on its representation in the kernel space. CKSC focuses on reconstructing each data sample via weighted contributions which are confident in its corresponding class of data. We employ novel discriminative terms to apply this scheme to both training and test frameworks in our algorithm. This specific design increases the consistency of these optimization frameworks and improves the discriminative performance in the recall phase. In addition, CKSC directly employs the supervised information in its dictionary learning framework to enhance the discriminative structure of the dictionary. For empirical evaluations, we implement our CKSC algorithm on multivariate time-series benchmarks such as DynTex++ and UTKinect. Our claims regarding the superior performance of the proposed algorithm are justified throughout comparing its classification results to the state-of-the-art K-SRC algorithms.
Recently, label consistent k-svd (LC-KSVD) algorithm has been successfully applied in image classification. The objective function of LC-KSVD is consisted of reconstruction error, classification error and discriminative sparse codes error with L0-norm sparse regularization term. The L0-norm, however, leads to NP-hard problem. Despite some methods such as orthogonal matching pursuit can help solve this problem to some extent, it is quite difficult to find the optimum sparse solution. To overcome this limitation, we propose a label embedded dictionary learning (LEDL) method to utilise the L1-norm as the sparse regularization term so that we can avoid the hard-to-optimize problem by solving the convex optimization problem. Alternating direction method of multipliers and blockwise coordinate descent algorithm are then exploited to optimize the corresponding objective function. Extensive experimental results on six benchmark datasets illustrate that the proposed algorithm has achieved superior performance compared to some conventional classification algorithms.
Discriminative Dictionary Learning (DL) methods have been widely advocated for image classification problems. To further sharpen their discriminative capabilities, most state-of-the-art DL methods have additional constraints included in the learning stages. These various constraints, however, lead to additional computational complexity. We hence propose an efficient Discriminative Convolutional Analysis Dictionary Learning (DCADL) method, as a lower cost Discriminative DL framework, to both characterize the image structures and refine the interclass structure representations. The proposed DCADL jointly learns a convolutional analysis dictionary and a universal classifier, while greatly reducing the time complexity in both training and testing phases, and achieving a competitive accuracy, thus demonstrating great performance in many experiments with standard databases.
There exist many approaches for description and recognition of unseen classes in datasets. Nevertheless, it becomes a challenging problem when we deal with multivariate time-series (MTS) (e.g., motion data), where we cannot apply the vectorial algorithms directly to the inputs. In this work, we propose a novel multiple-kernel dictionary learning (MKD) which learns semantic attributes based on specific combinations of MTS dimensions in the feature space. Hence, MKD can fully/partially reconstructs the unseen classes based on the training data (seen classes). Furthermore, we obtain sparse encodings for unseen classes based on the learned MKD attributes, and upon which we propose a simple but effective incremental clustering algorithm to categorize the unseen MTS classes in an unsupervised way. According to the empirical evaluation of our MKD framework on real benchmarks, it provides an interpretable reconstruction of unseen MTS data as well as a high performance regarding their online clustering.