Trac D. Tran

Samuel W. Remedios, Shuo Han, Yuan Xue et al.

In 2D multi-slice magnetic resonance (MR) acquisition, the through-plane signals are typically of lower resolution than the in-plane signals. While contemporary super-resolution (SR) methods aim to recover the underlying high-resolution volume, the estimated high-frequency information is implicit via end-to-end data-driven training rather than being explicitly stated and sought. To address this, we reframe the SR problem statement in terms of perfect reconstruction filter banks, enabling us to identify and directly estimate the missing information. In this work, we propose a two-stage approach to approximate the completion of a perfect reconstruction filter bank corresponding to the anisotropic acquisition of a particular scan. In stage 1, we estimate the missing filters using gradient descent and in stage 2, we use deep networks to learn the mapping from coarse coefficients to detail coefficients. In addition, the proposed formulation does not rely on external training data, circumventing the need for domain shift correction. Under our approach, SR performance is improved particularly in "slice gap" scenarios, likely due to the constrained solution space imposed by the framework.

Wentao Zhu, Xiang Xiang, Trac D. Tran et al.

Mass segmentation provides effective morphological features which are important for mass diagnosis. In this work, we propose a novel end-to-end network for mammographic mass segmentation which employs a fully convolutional network (FCN) to model a potential function, followed by a CRF to perform structured learning. Because the mass distribution varies greatly with pixel position, the FCN is combined with a position priori. Further, we employ adversarial training to eliminate over-fitting due to the small sizes of mammogram datasets. Multi-scale FCN is employed to improve the segmentation performance. Experimental results on two public datasets, INbreast and DDSM-BCRP, demonstrate that our end-to-end network achieves better performance than state-of-the-art approaches. \footnote{https://github.com/wentaozhu/adversarial-deep-structural-networks.git}

Dhananjaya Jayasundara, Sudarshan Rajagopalan, Yasiru Ranasinghe et al.

Implicit Neural Representations (INRs) are increasingly recognized as a versatile data modality for representing discretized signals, offering benefits such as infinite query resolution and reduced storage requirements. Existing signal compression approaches for INRs typically employ one of two strategies: 1. direct quantization with entropy coding of the trained INR; 2. deriving a latent code on top of the INR through a learnable transformation. Thus, their performance is heavily dependent on the quantization and entropy coding schemes employed. In this paper, we introduce SINR, an innovative compression algorithm that leverages the patterns in the vector spaces formed by weights of INRs. We compress these vector spaces using a high-dimensional sparse code within a dictionary. Further analysis reveals that the atoms of the dictionary used to generate the sparse code do not need to be learned or transmitted to successfully recover the INR weights. We demonstrate that the proposed approach can be integrated with any existing INR-based signal compression technique. Our results indicate that SINR achieves substantial reductions in storage requirements for INRs across various configurations, outperforming conventional INR-based compression baselines. Furthermore, SINR maintains high-quality decoding across diverse data modalities, including images, occupancy fields, and Neural Radiance Fields.

Yang Jiao, Guangming Shi, Trac D. Tran

Optical flow estimation with occlusion or large displacement is a problematic challenge due to the lost of corresponding pixels between consecutive frames. In this paper, we discover that the lost information is related to a large quantity of motion features (more than 40%) computed from the popular discriminative cost-volume feature would completely vanish due to invalid sampling, leading to the low efficiency of optical flow learning. We call this phenomenon the Vanishing Cost Volume Problem. Inspired by the fact that local motion tends to be highly consistent within a short temporal window, we propose a novel iterative Motion Feature Recovery (MFR) method to address the vanishing cost volume via modeling motion consistency across multiple frames. In each MFR iteration, invalid entries from original motion features are first determined based on the current flow. Then, an efficient network is designed to adaptively learn the motion correlation to recover invalid features for lost-information restoration. The final optical flow is then decoded from the recovered motion features. Experimental results on Sintel and KITTI show that our method achieves state-of-the-art performances. In fact, MFR currently ranks second on Sintel public website.

Yang Jiao, Yi Niu, Trac D. Tran et al.

In 2D+3D facial expression recognition (FER), existing methods generate multi-view geometry maps to enhance the depth feature representation. However, this may introduce false estimations due to local plane fitting from incomplete point clouds. In this paper, we propose a novel Map Generation technique from the viewpoint of information theory, to boost the slight 3D expression differences from strong personality variations. First, we examine the HDR depth data to extract the discriminative dynamic range $r_{dis}$, and maximize the entropy of $r_{dis}$ to a global optimum. Then, to prevent the large deformation caused by over-enhancement, we introduce a depth distortion constraint and reduce the complexity from $O(KN^2)$ to $O(KNτ)$. Furthermore, the constrained optimization is modeled as a $K$-edges maximum weight path problem in a directed acyclic graph, and we solve it efficiently via dynamic programming. Finally, we also design an efficient Facial Attention structure to automatically locate subtle discriminative facial parts for multi-scale learning, and train it with a proposed loss function $\mathcal{L}_{FA}$ without any facial landmarks. Experimental results on different datasets show that the proposed method is effective and outperforms the state-of-the-art 2D+3D FER methods in both FER accuracy and the output entropy of the generated maps.

Yang Jiao, Trac D. Tran, Guangming Shi

This paper addresses the challenging unsupervised scene flow estimation problem by jointly learning four low-level vision sub-tasks: optical flow $\textbf{F}$, stereo-depth $\textbf{D}$, camera pose $\textbf{P}$ and motion segmentation $\textbf{S}$. Our key insight is that the rigidity of the scene shares the same inherent geometrical structure with object movements and scene depth. Hence, rigidity from $\textbf{S}$ can be inferred by jointly coupling $\textbf{F}$, $\textbf{D}$ and $\textbf{P}$ to achieve more robust estimation. To this end, we propose a novel scene flow framework named EffiScene with efficient joint rigidity learning, going beyond the existing pipeline with independent auxiliary structures. In EffiScene, we first estimate optical flow and depth at the coarse level and then compute camera pose by Perspective-$n$-Points method. To jointly learn local rigidity, we design a novel Rigidity From Motion (RfM) layer with three principal components: \emph{}{(i)} correlation extraction; \emph{}{(ii)} boundary learning; and \emph{}{(iii)} outlier exclusion. Final outputs are fused based on the rigid map $M_R$ from RfM at finer levels. To efficiently train EffiScene, two new losses $\mathcal{L}_{bnd}$ and $\mathcal{L}_{unc}$ are designed to prevent trivial solutions and to regularize the flow boundary discontinuity. Extensive experiments on scene flow benchmark KITTI show that our method is effective and significantly improves the state-of-the-art approaches for all sub-tasks, i.e. optical flow ($5.19 \rightarrow 4.20$), depth estimation ($3.78 \rightarrow 3.46$), visual odometry ($0.012 \rightarrow 0.011$) and motion segmentation ($0.57 \rightarrow 0.62$).

Akshay Rangamani, Nam H. Nguyen, Abhishek Kumar et al.

It has been empirically observed that the flatness of minima obtained from training deep networks seems to correlate with better generalization. However, for deep networks with positively homogeneous activations, most measures of sharpness/flatness are not invariant to rescaling of the network parameters, corresponding to the same function. This means that the measure of flatness/sharpness can be made as small or as large as possible through rescaling, rendering the quantitative measures meaningless. In this paper we show that for deep networks with positively homogenous activations, these rescalings constitute equivalence relations, and that these equivalence relations induce a quotient manifold structure in the parameter space. Using this manifold structure and an appropriate metric, we propose a Hessian-based measure for flatness that is invariant to rescaling. We use this new measure to confirm the proposition that Large-Batch SGD minima are indeed sharper than Small-Batch SGD minima.

Luoluo Liu, Sang Peter Chin, Trac D. Tran

Bagging, a powerful ensemble method from machine learning, improves the performance of unstable predictors. Although the power of Bagging has been shown mostly in classification problems, we demonstrate the success of employing Bagging in sparse regression over the baseline method (L1 minimization). The framework employs the generalized version of the original Bagging with various bootstrap ratios. The performance limits associated with different choices of bootstrap sampling ratio L/m and number of estimates K is analyzed theoretically. Simulation shows that the proposed method yields state-of-the-art recovery performance, outperforming L1 minimization and Bolasso in the challenging case of low levels of measurements. A lower L/m ratio (60% - 90%) leads to better performance, especially with a small number of measurements. With the reduced sampling rate, SNR improves over the original Bagging by up to 24%. With a properly chosen sampling ratio, a reasonably small number of estimates K = 30 gives satisfying result, even though increasing K is discovered to always improve or at least maintain the performance.

Dung N. Tran, Trac D. Tran, Lam Nguyen

Ultra-wideband (UWB) radar systems nowadays typical operate in the low frequency spectrum to achieve penetration capability. However, this spectrum is also shared by many others communication systems, which causes missing information in the frequency bands. To recover this missing spectral information, we propose a generative adversarial network, called SARGAN, that learns the relationship between original and missing band signals by observing these training pairs in a clever way. Initial results shows that this approach is promising in tackling this challenging missing band problem.

Luoluo Liu, Sang Peter Chin, Trac D. Tran

Classical signal recovery based on $\ell_1$ minimization solves the least squares problem with all available measurements via sparsity-promoting regularization. In practice, it is often the case that not all measurements are available or required for recovery. Measurements might be corrupted/missing or they arrive sequentially in streaming fashion. In this paper, we propose a global sparse recovery strategy based on subsets of measurements, named JOBS, in which multiple measurements vectors are generated from the original pool of measurements via bootstrapping, and then a joint-sparse constraint is enforced to ensure support consistency among multiple predictors. The final estimate is obtained by averaging over the $K$ predictors. The performance limits associated with different choices of number of bootstrap samples $L$ and number of estimates $K$ is analyzed theoretically. Simulation results validate some of the theoretical analysis, and show that the proposed method yields state-of-the-art recovery performance, outperforming $\ell_1$ minimization and a few other existing bootstrap-based techniques in the challenging case of low levels of measurements and is preferable over other bagging-based methods in the streaming setting since it performs better with small $K$ and $L$ for data-sets with large sizes.

Akshay Rangamani, Anirbit Mukherjee, Amitabh Basu et al.

In "Dictionary Learning" one tries to recover incoherent matrices $A^* \in \mathbb{R}^{n \times h}$ (typically overcomplete and whose columns are assumed to be normalized) and sparse vectors $x^* \in \mathbb{R}^h$ with a small support of size $h^p$ for some $0 <p < 1$ while having access to observations $y \in \mathbb{R}^n$ where $y = A^*x^*$. In this work we undertake a rigorous analysis of whether gradient descent on the squared loss of an autoencoder can solve the dictionary learning problem. The "Autoencoder" architecture we consider is a $\mathbb{R}^n \rightarrow \mathbb{R}^n$ mapping with a single ReLU activation layer of size $h$. Under very mild distributional assumptions on $x^*$, we prove that the norm of the expected gradient of the standard squared loss function is asymptotically (in sparse code dimension) negligible for all points in a small neighborhood of $A^*$. This is supported with experimental evidence using synthetic data. We also conduct experiments to suggest that $A^*$ is a local minimum. Along the way we prove that a layer of ReLU gates can be set up to automatically recover the support of the sparse codes. This property holds independent of the loss function. We believe that it could be of independent interest.

Dong Yang, Tao Xiong, Daguang Xu et al.

Automatic localization and labeling of vertebra in 3D medical images plays an important role in many clinical tasks, including pathological diagnosis, surgical planning and postoperative assessment. However, the unusual conditions of pathological cases, such as the abnormal spine curvature, bright visual imaging artifacts caused by metal implants, and the limited field of view, increase the difficulties of accurate localization. In this paper, we propose an automatic and fast algorithm to localize and label the vertebra centroids in 3D CT volumes. First, we deploy a deep image-to-image network (DI2IN) to initialize vertebra locations, employing the convolutional encoder-decoder architecture together with multi-level feature concatenation and deep supervision. Next, the centroid probability maps from DI2IN are iteratively evolved with the message passing schemes based on the mutual relation of vertebra centroids. Finally, the localization results are refined with sparsity regularization. The proposed method is evaluated on a public dataset of 302 spine CT volumes with various pathologies. Our method outperforms other state-of-the-art methods in terms of localization accuracy. The run time is around 3 seconds on average per case. To further boost the performance, we retrain the DI2IN on additional 1000+ 3D CT volumes from different patients. To the best of our knowledge, this is the first time more than 1000 3D CT volumes with expert annotation are adopted in experiments for the anatomic landmark detection tasks. Our experimental results show that training with such a large dataset significantly improves the performance and the overall identification rate, for the first time by our knowledge, reaches 90 %.

Feng Wang, Xiang Xiang, Chang Liu et al.

Limited labeled data are available for the research of estimating facial expression intensities. For instance, the ability to train deep networks for automated pain assessment is limited by small datasets with labels of patient-reported pain intensities. Fortunately, fine-tuning from a data-extensive pre-trained domain, such as face verification, can alleviate this problem. In this paper, we propose a network that fine-tunes a state-of-the-art face verification network using a regularized regression loss and additional data with expression labels. In this way, the expression intensity regression task can benefit from the rich feature representations trained on a huge amount of data for face verification. The proposed regularized deep regressor is applied to estimate the pain expression intensity and verified on the widely-used UNBC-McMaster Shoulder-Pain dataset, achieving the state-of-the-art performance. A weighted evaluation metric is also proposed to address the imbalance issue of different pain intensities.

Xiaoxia Sun, Nasser M. Nasrabadi, Trac D. Tran

In this paper, we describe the deep sparse coding network (SCN), a novel deep network that encodes intermediate representations with nonnegative sparse coding. The SCN is built upon a number of cascading bottleneck modules, where each module consists of two sparse coding layers with relatively wide and slim dictionaries that are specialized to produce high dimensional discriminative features and low dimensional representations for clustering, respectively. During training, both the dictionaries and regularization parameters are optimized with an end-to-end supervised learning algorithm based on multilevel optimization. Effectiveness of an SCN with seven bottleneck modules is verified on several popular benchmark datasets. Remarkably, with few parameters to learn, our SCN achieves 5.81% and 19.93% classification error rate on CIFAR-10 and CIFAR-100, respectively.

Xiang Xiang, Trac D. Tran

Limited annotated data available for the recognition of facial expression and action units embarrasses the training of deep networks, which can learn disentangled invariant features. However, a linear model with just several parameters normally is not demanding in terms of training data. In this paper, we propose an elegant linear model to untangle confounding factors in challenging realistic multichannel signals such as 2D face videos. The simple yet powerful model does not rely on huge training data and is natural for recognizing facial actions without explicitly disentangling the identity. Base on well-understood intuitive linear models such as Sparse Representation based Classification (SRC), previous attempts require a prepossessing of explicit decoupling which is practically inexact. Instead, we exploit the low-rank property across frames to subtract the underlying neutral faces which are modeled jointly with sparse representation on the action components with group sparsity enforced. On the extended Cohn-Kanade dataset (CK+), our one-shot automatic method on raw face videos performs as competitive as SRC applied on manually prepared action components and performs even better than SRC in terms of true positive rate. We apply the model to the even more challenging task of facial action unit recognition, verified on the MPI Face Video Database (MPI-VDB) achieving a decent performance. All the programs and data have been made publicly available.

Wentao Zhu, Xiang Xiang, Trac D. Tran et al.

Mass segmentation is an important task in mammogram analysis, providing effective morphological features and regions of interest (ROI) for mass detection and classification. Inspired by the success of using deep convolutional features for natural image analysis and conditional random fields (CRF) for structural learning, we propose an end-to-end network for mammographic mass segmentation. The network employs a fully convolutional network (FCN) to model potential function, followed by a CRF to perform structural learning. Because the mass distribution varies greatly with pixel position, the FCN is combined with position priori for the task. Due to the small size of mammogram datasets, we use adversarial training to control over-fitting. Four models with different convolutional kernels are further fused to improve the segmentation results. Experimental results on two public datasets, INbreast and DDSM-BCRP, show that our end-to-end network combined with adversarial training achieves the-state-of-the-art results.

Xiang Xiang, Trac D. Tran

In this paper, we deal with two challenges for measuring the similarity of the subject identities in practical video-based face recognition - the variation of the head pose in uncontrolled environments and the computational expense of processing videos. Since the frame-wise feature mean is unable to characterize the pose diversity among frames, we define and preserve the overall pose diversity and closeness in a video. Then, identity will be the only source of variation across videos since the pose varies even within a single video. Instead of simply using all the frames, we select those faces whose pose point is closest to the centroid of the K-means cluster containing that pose point. Then, we represent a video as a bag of frame-wise deep face features while the number of features has been reduced from hundreds to K. Since the video representation can well represent the identity, now we measure the subject similarity between two videos as the max correlation among all possible pairs in the two bags of features. On the official 5,000 video-pairs of the YouTube Face dataset for face verification, our algorithm achieves a comparable performance with VGG-face that averages over deep features of all frames. Other vision tasks can also benefit from the generic idea of employing geometric cues to improve the descriptiveness of deep features.

Minh Dao, Xiang Xiang, Bulent Ayhan et al.

In this paper, we propose a burnscar detection model for hyperspectral imaging (HSI) data. The proposed model contains two-processing steps in which the first step separate and then suppress the cloud information presenting in the data set using an RPCA algorithm and the second step detect the burnscar area in the low-rank component output of the first step. Experiments are conducted on the public MODIS dataset available at NASA official website.

Xiaoxia Sun, Nasser M. Nasrabadi, Trac D. Tran

Sparse representation-based classifiers have shown outstanding accuracy and robustness in image classification tasks even with the presence of intense noise and occlusion. However, it has been discovered that the performance degrades significantly either when test image is not aligned with the dictionary atoms or the dictionary atoms themselves are not aligned with each other, in which cases the sparse linear representation assumption fails. In this paper, having both training and test images misaligned, we introduce a novel sparse coding framework that is able to efficiently adapt the dictionary atoms to the test image via large displacement optical flow. In the proposed algorithm, every dictionary atom is automatically aligned with the input image and the sparse code is then recovered using the adapted dictionary atoms. A corresponding supervised dictionary learning algorithm is also developed for the proposed framework. Experimental results on digit datasets recognition verify the efficacy and robustness of the proposed algorithm.

Hojjat S. Mousavi, Vishal Monga, Trac D. Tran

In this letter, we address sparse signal recovery using spike and slab priors. In particular, we focus on a Bayesian framework where sparsity is enforced on reconstruction coefficients via probabilistic priors. The optimization resulting from spike and slab prior maximization is known to be a hard non-convex problem, and existing solutions involve simplifying assumptions and/or relaxations. We propose an approach called Iterative Convex Refinement (ICR) that aims to solve the aforementioned optimization problem directly allowing for greater generality in the sparse structure. Essentially, ICR solves a sequence of convex optimization problems such that sequence of solutions converges to a sub-optimal solution of the original hard optimization problem. We propose two versions of our algorithm: a.) an unconstrained version, and b.) with a non-negativity constraint on sparse coefficients, which may be required in some real-world problems. Experimental validation is performed on both synthetic data and for a real-world image recovery problem, which illustrates merits of ICR over state of the art alternatives.

Xiaoxia Sun, Nasser M. Nasrabadi, Trac D. Tran

Sparse representation models a signal as a linear combination of a small number of dictionary atoms. As a generative model, it requires the dictionary to be highly redundant in order to ensure both a stable high sparsity level and a low reconstruction error for the signal. However, in practice, this requirement is usually impaired by the lack of labelled training samples. Fortunately, previous research has shown that the requirement for a redundant dictionary can be less rigorous if simultaneous sparse approximation is employed, which can be carried out by enforcing various structured sparsity constraints on the sparse codes of the neighboring pixels. In addition, numerous works have shown that applying a variety of dictionary learning methods for the sparse representation model can also improve the classification performance. In this paper, we highlight the task-driven dictionary learning algorithm, which is a general framework for the supervised dictionary learning method. We propose to enforce structured sparsity priors on the task-driven dictionary learning method in order to improve the performance of the hyperspectral classification. Our approach is able to benefit from both the advantages of the simultaneous sparse representation and those of the supervised dictionary learning. We enforce two different structured sparsity priors, the joint and Laplacian sparsity, on the task-driven dictionary learning method and provide the details of the corresponding optimization algorithms. Experiments on numerous popular hyperspectral images demonstrate that the classification performance of our approach is superior to sparse representation classifier with structured priors or the task-driven dictionary learning method.

Minh Dao, Nam H. Nguyen, Nasser M. Nasrabadi et al.

In this paper, we propose a general collaborative sparse representation framework for multi-sensor classification, which takes into account the correlations as well as complementary information between heterogeneous sensors simultaneously while considering joint sparsity within each sensor's observations. We also robustify our models to deal with the presence of sparse noise and low-rank interference signals. Specifically, we demonstrate that incorporating the noise or interference signal as a low-rank component in our models is essential in a multi-sensor classification problem when multiple co-located sources/sensors simultaneously record the same physical event. We further extend our frameworks to kernelized models which rely on sparsely representing a test sample in terms of all the training samples in a feature space induced by a kernel function. A fast and efficient algorithm based on alternative direction method is proposed where its convergence to an optimal solution is guaranteed. Extensive experiments are conducted on several real multi-sensor data sets and results are compared with the conventional classifiers to verify the effectiveness of the proposed methods.

Xiang Xiang, Minh Dao, Gregory D. Hager et al.

In this paper, we design a Collaborative-Hierarchical Sparse and Low-Rank (C-HiSLR) model that is natural for recognizing human emotion in visual data. Previous attempts require explicit expression components, which are often unavailable and difficult to recover. Instead, our model exploits the lowrank property over expressive facial frames and rescue inexact sparse representations by incorporating group sparsity. For the CK+ dataset, C-HiSLR on raw expressive faces performs as competitive as the Sparse Representation based Classification (SRC) applied on manually prepared emotions. C-HiSLR performs even better than SRC in terms of true positive rate.

Yuanming Suo, Minh Dao, Umamahesh Srinivas et al.

Sparsity driven signal processing has gained tremendous popularity in the last decade. At its core, the assumption is that the signal of interest is sparse with respect to either a fixed transformation or a signal dependent dictionary. To better capture the data characteristics, various dictionary learning methods have been proposed for both reconstruction and classification tasks. For classification particularly, most approaches proposed so far have focused on designing explicit constraints on the sparse code to improve classification accuracy while simply adopting $l_0$-norm or $l_1$-norm for sparsity regularization. Motivated by the success of structured sparsity in the area of Compressed Sensing, we propose a structured dictionary learning framework (StructDL) that incorporates the structure information on both group and task levels in the learning process. Its benefits are two-fold: (i) the label consistency between dictionary atoms and training data are implicitly enforced; and (ii) the classification performance is more robust in the cases of a small dictionary size or limited training data than other techniques. Using the subspace model, we derive the conditions for StructDL to guarantee the performance and show theoretically that StructDL is superior to $l_0$-norm or $l_1$-norm regularized dictionary learning for classification. Extensive experiments have been performed on both synthetic simulations and real world applications, such as face recognition and object classification, to demonstrate the validity of the proposed DL framework.

Xiaoxia Sun, Qing Qu, Nasser M. Nasrabadi et al.

Pixel-wise classification, where each pixel is assigned to a predefined class, is one of the most important procedures in hyperspectral image (HSI) analysis. By representing a test pixel as a linear combination of a small subset of labeled pixels, a sparse representation classifier (SRC) gives rather plausible results compared with that of traditional classifiers such as the support vector machine (SVM). Recently, by incorporating additional structured sparsity priors, the second generation SRCs have appeared in the literature and are reported to further improve the performance of HSI. These priors are based on exploiting the spatial dependencies between the neighboring pixels, the inherent structure of the dictionary, or both. In this paper, we review and compare several structured priors for sparse-representation-based HSI classification. We also propose a new structured prior called the low rank group prior, which can be considered as a modification of the low rank prior. Furthermore, we will investigate how different structured priors improve the result for the HSI classification.