Sparse Dictionary Learning Method Research Articles

Physics-informed machine learning of multi-source monitoring data sparsely measured within a 2D vertical cross-section

Conventional machine learning (ML) methods suffer from several limitations, e.g., overreliance on large training datasets and poor performance in extrapolating beyond observations. Geotechnical monitoring data at specific sites are multi-sourced (e.g., settlement and horizontal displacement data). Moreover, each source of monitoring data may vary temporally and be sparsely measured, e.g., within a two-dimensional (2D) geological cross-section. Thus, effectively learning multi-source and limited monitoring data is difficult using existing ML methods. To address this challenge, this study proposes a physics-informed ML method combining geotechnical numerical models (e.g., the finite element model (FEM)) with sparse dictionary learning (SDL) methods. It uses a range of probable numerical model results corresponding to multiple, temporally varying responses in a 2D spatial range to construct a “dictionary” in SDL and employs multi-source and limited monitoring data to identify a few “atoms” from the constructed dictionary to improve model predictions. An engineering project for embankment construction is used to illustrate the proposed approach. Our results indicate that the proposed approach effectively integrates FEM results with multi-source and sparsely measured monitoring data and improves the predictions of multiple spatio-temporally varying geotechnical responses significantly, particularly those at subsequent time steps and unmonitored spatial locations within a 2D vertical cross-section.

Nectarine Disease Identification Based on Color Features and Label Sparse Dictionary Learning with Hyperspectral Images

Fruit cracking and rust spots are common diseases of nectarines that seriously affect their yield and quality. Therefore, it is essential to construct fast and accurate disease-identification models for agricultural products. In this paper, a sparse dictionary learning method was proposed to realize the rapid and nondestructive identification of nectarine disease based on multiple color features combined with improved LK-SVD (Label K-Singular Value Decomposition). According to the color characteristics of the nectarine itself and the significant color differences existing in the three categories of nectarine (diseased, normal, and background parts), multiple color spaces of RGB, HSV, Lab, and YCbCr were studied. It was concluded that the G channel in RGB space, Y channel in YCbCr space, and L channel in Lab space can better distinguish the diseased part from the other parts. At the model-training stage, pixels of the diseased, normal, and background parts in the nectarine image were randomly selected as the initial training sets, and then, the neighboring image blocks of the pixels were selected to construct the feature vectors based on the above color space channels. An improved LK-SVD dictionary learning algorithm was proposed that integrated the category label into the process of dictionary learning, and thus, an over-complete feature dictionary with significant discrimination was obtained. At the model-testing stage, the orthogonal matching pursuit (OMP) algorithm was used for sparse reconstruction of the original data, which can obtain the classification categories based on the optimized feature dictionary. The experimental results show that the sparse dictionary learning method based on multi-color features combined with improved LK-SVD can identify fruit cracking and rust spot diseases of nectarines quickly and accurately, and the average overall classification accuracies were 92.06% and 88.98%, respectively, which were better than those of k-nearest neighbor (KNN), support vector machine (SVM), DeepLabV3+, and Unet++; the identification results of DeepLabV3+ and Unet++ were also relatively high, but their average time costs were much higher, requiring 126.46~265.65 s. It is demonstrated that this study can provide technical support for disease identification in agricultural products.

Robust Long-Term Visual Object Tracking via Low-Rank Sparse Learning for Re-Detection

The Discriminative Correlation Filter (DCF) has been universally recognized in visual object tracking, thanks to its excellent accuracy and high speed. Nevertheless, these DCF-based trackers perform poorly in long-term tracking. The reasons include the following aspects—first, they have low adaptability to significant appearance changes in long-term tracking and are prone to tracking failure; second, these trackers lack a practical re-detection module to find the target again after tracking failure. In our work, we propose a new long-term tracking strategy to solve these issues. First, we make the best of the static and dynamic information of the target by introducing the motion features to our long-term tracker and obtain a more robust tracker. Second, we introduce a low-rank sparse dictionary learning method for re-detection. This re-detection module can exploit a correlation among these training samples and alleviate the impact of occlusion and noise. Third, we propose a new reliability evaluation method to model an adaptive update, which can switch expediently between the tracking module and the re-detection module. Massive experiments demonstrate that our proposed approach has an obvious improvement in precision and success rate over these state-of-the-art trackers.

A framework to identify structured behavioral patterns within rodent spatial trajectories

Animal behavior is highly structured. Yet, structured behavioral patterns—or “statistical ethograms”—are not immediately apparent from the full spatiotemporal data that behavioral scientists usually collect. Here, we introduce a framework to quantitatively characterize rodent behavior during spatial (e.g., maze) navigation, in terms of movement building blocks or motor primitives. The hypothesis that we pursue is that rodent behavior is characterized by a small number of motor primitives, which are combined over time to produce open-ended movements. We assume motor primitives to be organized in terms of two sparsity principles: each movement is controlled using a limited subset of motor primitives (sparse superposition) and each primitive is active only for time-limited, time-contiguous portions of movements (sparse activity). We formalize this hypothesis using a sparse dictionary learning method, which we use to extract motor primitives from rodent position and velocity data collected during spatial navigation, and successively to reconstruct past trajectories and predict novel ones. Three main results validate our approach. First, rodent behavioral trajectories are robustly reconstructed from incomplete data, performing better than approaches based on standard dimensionality reduction methods, such as principal component analysis, or single sparsity. Second, the motor primitives extracted during one experimental session generalize and afford the accurate reconstruction of rodent behavior across successive experimental sessions in the same or in modified mazes. Third, in our approach the number of motor primitives associated with each maze correlates with independent measures of maze complexity, hence showing that our formalism is sensitive to essential aspects of task structure. The framework introduced here can be used by behavioral scientists and neuroscientists as an aid for behavioral and neural data analysis. Indeed, the extracted motor primitives enable the quantitative characterization of the complexity and similarity between different mazes and behavioral patterns across multiple trials (i.e., habit formation). We provide example uses of this computational framework, showing how it can be used to identify behavioural effects of maze complexity, analyze stereotyped behavior, classify behavioral choices and predict place and grid cell displacement in novel environments.

Sparse deep dictionary learning identifies differences of time-varying functional connectivity in brain neuro-developmental study

Recently, the focus of functional connectivity analysis of human brain has shifted from merely revealing the inter-regional functional correlation over the entire scan duration to capturing the time-varying information of brain networks and characterizing time-resolved reoccurring patterns of connectivity. Much effort has been invested into developing approaches that can track changes in re-occurring patterns of functional connectivity over time. In this paper, we propose a sparse deep dictionary learning method to characterize the essential differences of reoccurring patterns of time-varying functional connectivity between different age groups. The proposed method combines both the interpretability of sparse dictionary learning and the capability of extracting sparse nonlinear higher-level features in the latent space of sparse deep autoencoder. In other words, it learns a sparse dictionary of the original data by considering the nonlinear representation of the data in the encoder layer based on a sparse deep autoencoder. In this way, the nonlinear structure and higher-level features of the data can be captured by deep dictionary learning. The proposed method is applied to the analysis of the Philadelphia Neurodevelopmental Cohort. It shows that there exist essential differences in the reoccurrence patterns of function connectivity between child and young adult groups. Specially, children have more diffusive functional connectivity patterns while young adults possess more focused functional connectivity patterns, and the brain function transits from undifferentiated systems to specialized neural networks with the growth.

Quality Control of Additively Manufactured Metallic Structures with Machine Learning of Thermography Images

Additive manufacturing (AM) of high-strength metals is currently based on the laser powder bed fusion (LPBF) process, which can introduce internal material flaws, such as pores and anisotropy. Quality control (QC) requires nondestructive evaluation of actual AM structures. Flash thermography is a potentially promising QC technique because it is scalable to arbitrary structure size. However, the detection sensitivity of this method is limited by noise. We investigate separation of signal from noise in thermography images using several machine learning (ML) methods, including new spatial–temporal blind source separation and spatial–temporal sparse dictionary learning methods. Performance of the ML methods is benchmarked using thermography data obtained from imaging stainless steel 316L and Inconel 718 specimens produced by the LPBF method with imprinted calibrated porosity defects. The ML methods are ranked by F-score and execution runtime. The ML methods with higher accuracy require a longer runtime. However, this runtime is sufficiently short to perform QC within a realistic time frame.

Multi-Needle Detection in 3D Ultrasound Images Using Unsupervised Order-Graph Regularized Sparse Dictionary Learning.

Accurate and automatic multi-needle detection in three-dimensional (3D) ultrasound (US) is a key step of treatment planning for US-guided brachytherapy. However, most current studies are concentrated on single-needle detection by only using a small number of images with a needle, regardless of the massive database of US images without needles. In this paper, we propose a workflow for multi-needle detection by considering the images without needles as auxiliary. Concretely, we train position-specific dictionaries on 3D overlapping patches of auxiliary images, where we develop an enhanced sparse dictionary learning method by integrating spatial continuity of 3D US, dubbed order-graph regularized dictionary learning. Using the learned dictionaries, target images are reconstructed to obtain residual pixels which are then clustered in every slice to yield centers. With the obtained centers, regions of interest (ROIs) are constructed via seeking cylinders. Finally, we detect needles by using the random sample consensus algorithm per ROI and then locate the tips by finding the sharp intensity drops along the detected axis for every needle. Extensive experiments were conducted on a phantom dataset and a prostate dataset of 70/21 patients without/with needles. Visualization and quantitative results show the effectiveness of our proposed workflow. Specifically, our method can correctly detect 95% of needles with a tip location error of 1.01 mm on the prostate dataset. This technique provides accurate multi-needle detection for US-guided HDR prostate brachytherapy, facilitating the clinical workflow.

Dictionary Learning for Two-Dimensional Kendall Shapes

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between algorithmic simplicity and faithfulness with respect to the nonlinear geometric structure of Kendall's shape space. Remarkably, it boils down to a classical dictionary learning formulation modified using complex weights. Existing dictionary learning methods extended to nonlinear spaces map the manifold either to a reproducing kernel Hilbert space or to a tangent space. The first approach is unnecessarily heavy in the case of Kendall's shape space and causes the geometrical understanding of shapes to be lost, while the second one induces distortions and theoretical complexity. Our approach does not suffer from these drawbacks. Instead of embedding the shape space into a linear space, we rely on the hyperplane of centered configurations, including preshapes from which shapes are defined as rotation orbits. In this linear space, the dictionary atoms are scaled and rotated using complex weights before summation. Furthermore, our formulation is more general than Kendall's original one: it applies to discretely defined configurations of landmarks as well as continuously defined interpolating curves. We implemented our algorithm by adapting the method of optimal directions combined to a Cholesky-optimized order recursive matching pursuit. An interesting feature of our shape dictionary is that it produces visually realistic atoms, while guaranteeing reconstruction accuracy. Its efficiency can mostly be attributed to a clear formulation of the framework with complex numbers. We illustrate the strong potential of our approach for the characterization of datasets of shapes up to similitudes and the analysis of patterns in deforming two-dimensional shapes.

Unsupervised feature selection based on joint spectral learning and general sparse regression

Unsupervised feature selection is an important machine learning task since the manual annotated data are dramatically expensive to obtain and therefore very limited. However, due to the existence of noise and outliers in different data samples, feature selection without the help of discriminant information embedded in the annotated data is quite challenging. To relieve these limitations, we investigate the embedding of spectral learning into a general sparse regression framework for unsupervised feature selection. Generally, the proposed general spectral sparse regression (GSSR) method handles the outlier features by learning the joint sparsity and the noisy features by preserving the local structures of data, jointly. Specifically, GSSR is conducted in two stages. First, the classic sparse dictionary learning method is used to build the bases of original data. After that, the original data are project to the basis space by learning a new representation via GSSR. In GSSR, robust loss function $$\ell _{2,r}{-}{norm}(0<r\le 2)$$ and $$\ell _{2,p}-{norm}(0<p\le 1)$$ instead of the traditional F norm and least square loss function are simultaneously considered as the reconstruction term and sparse regularization term for sparse regression. Furthermore, the local topological structures of the new representations are preserved by spectral learning based on the Laplacian term. The overall objective function in GSSR is optimized and proved to be converging. Experimental results on several publicly datasets have demonstrated the validity of our algorithm, which outperformed the state-of-the-art feature selections in terms of classification performance.

Hyperspectral Anomaly Detection via Sparse Dictionary Learning Method of Capped Norm

Hyperspectral anomaly detection is a research hot spot in the field of remote sensing. It can distinguish abnormal targets from the scene just by utilizing the spectral differences and requiring no prior information. A series of anomaly detectors based on Reed–Xiaoli methods are very important and typical algorithms in this research area, which generally have the hypothesis about background subject to the Gaussian distribution. However, this assumption is inaccurate to describe a hyperspectral image with a complex scene in practice. Besides, due to the unavoidable existence of abnormal targets, background statistics will be affected which will reduce the detection performance. To address these problems, we propose a sparse dictionary learning method by using a capped norm to realize hyperspectral anomaly detection. Moreover, a new training data selection strategy based on clustering technique is also proposed to learn a more representative background dictionary. The main contributions are concluded in threefold: 1) neither making any assumptions on the background distribution nor computing the covariance matrix, the proposed method is more adaptive to all kinds of complex hyperspectral images in practice; 2) owing to the good qualities of the capped norm, the learned sparse background dictionary is resistant to the effect of anomalies and has stronger distinctiveness to anomalies from background; 3) without using the traditional sliding hollow window technique, the proposed method is more effective to detect different sizes of abnormal targets. The extensive experiments on four commonly used real-world hyperspectral images demonstrate the effectiveness of the proposed method and show its superiority over the benchmark methods.

Mutually exclusive-KSVD: Learning a discriminative dictionary for hyperspectral image classification

Abstract Sparse representation and dictionary learning methods have been successfully applied in classification of hyperspectral images (HSIs). However, when the number of training data is insufficient which is widely happened in HSI classification, the learned sparse representation is generally insufficient and the corresponding performances would be significantly degraded. To address the above problem, in this paper, we propose a novel dictionary learning method, namely mutually exclusive K-SVD. We construct a mutual exclusion term for the dictionary by decomposing each class of sub-dictionary into positive and negative categories. Therefore, the learned sparse codes not only consider the within-class consistency, but also between-class mutual exclusion, thereby resulting in improved classification performance with limited training samples. Furthermore, in the testing phase, we utilize the multiscale strategy for each pixel instead of pixel-wise coding to make full use of the spatial features of the image and further improve the classification accuracy. Experimental results demonstrate that the proposed algorithm outperforms state-of-the art algorithms in both qualitative and quantitative evaluations.

Experimental Comparisons of Sparse Dictionary Learning and Independent Component Analysis for Brain Network Inference From fMRI Data.

In this work, we conduct comprehensive comparisons between four variants of independent component analysis (ICA) methods and three variants of sparse dictionary learning (SDL) methods, both at the subject-level, by using synthesized fMRI data with ground-truth. Our results showed that ICA methods perform very well and slightly better than SDL methods when functional networks' spatial overlaps are minor, but ICA methods have difficulty in differentiating functional networks with moderate or significant spatial overlaps. In contrast, the SDL algorithms perform consistently well no matter how functional networks spatially overlap, and importantly, SDL methods are significantly better than ICA methods when spatial overlaps between networks are moderate or severe. This work offers empirical better understanding of ICA and SDL algorithms in inferring functional networks from fMRI data and provides new guidelines and caveats when constructing and interpreting functional networks in the era of fMRI-based connectomics.

Single Image Rain Streak Decomposition Using Layer Priors.

Rain streaks impair visibility of an image and introduce undesirable interference that can severely affect the performance of computer vision and image analysis systems. Rain streak removal algorithms try to recover a rain streak free background scene. In this paper, we address the problem of rain streak removal from a single image by formulating it as a layer decomposition problem, with a rain streak layer superimposed on a background layer containing the true scene content. Existing decomposition methods that address this problem employ either sparse dictionary learning methods or impose a low rank structure on the appearance of the rain streaks. While these methods can improve the overall visibility, their performance can often be unsatisfactory, for they tend to either over-smooth the background images or generate -images that still contain noticeable rain streaks. To address the problems, we propose a method that imposes priors for both the background and rain streak layers. These priors are based on Gaussian mixture models learned on small patches that can accommodate a variety of background appearances as well as the appearance of the rain streaks. Moreover, we introduce a structure residue recovery step to further separate the background residues and improve the decomposition quality. Quantitative evaluation shows our method outperforms existing methods by a large margin. We overview our method and demonstrate its effectiveness over prior work on a number of examples.

EMPOWERING CORTICAL THICKNESS MEASURES IN CLINICAL DIAGNOSIS OF ALZHEIMER'S DISEASE WITH SPHERICAL SPARSE CODING.

Cortical thickness estimation performed in vivo via magnetic resonance imaging (MRI) is an important technique for the diagnosis and understanding of the progression of Alzheimer's disease (AD). Directly using raw cortical thickness measures as features with Support Vector Machine (SVM) for clinical group classification only yields modest results since brain areas are not equally atrophied during AD progression. Therefore, feature reduction is generally required to retain only the most relevant features for the final classification. In this paper, a spherical sparse coding and dictionary learning method is proposed and it achieves relatively high classification results on publicly available data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) 2 dataset (N = 201) which contains structural MRI data of four clinical groups: cognitive unimpaired (CU), early mild cognitive impairment (EMCI), later MCI (LMCI) and AD. The proposed framework takes the estimated cortical thickness and the spherical parameterization computed by FreeSurfer as inputs and constructs weighted patches in the spherical parameter domain of the cortical surface. Then sparse coding is applied to the resulting surface patch features, followed by max-pooling to extract the final feature sets. Finally, SVM is employed for binary group classifications. The results show the superiority of the proposed method over other cortical morphometry systems and offer a different way to study the early identification and prevention of AD.

Multiscale and Multitopic Sparse Representation for Multisensor Infrared Image Superresolution

Methods based on sparse coding have been successfully used in single-image superresolution (SR) reconstruction. However, the traditional sparse representation-based SR image reconstruction for infrared (IR) images usually suffers from three problems. First, IR images always lack detailed information. Second, a traditional sparse dictionary is learned from patches with a fixed size, which may not capture the exact information of the images and may ignore the fact that images naturally come at different scales in many cases. Finally, traditional sparse dictionary learning methods aim at learning a universal and overcomplete dictionary. However, many different local structural patterns exist. One dictionary is inadequate in capturing all of the different structures. We propose a novel IR image SR method to overcome these problems. First, we combine the information from multisensors to improve the resolution of the IR image. Then, we use multiscale patches to represent the image in a more efficient manner. Finally, we partition the natural images into documents and group such documents to determine the inherent topics and to learn the sparse dictionary of each topic. Extensive experiments validate that using the proposed method yields better results in terms of quantitation and visual perception than many state-of-the-art algorithms.

Brain tumor classification and segmentation using sparse coding and dictionary learning.

This paper presents a novel fully automatic framework for multi-class brain tumor classification and segmentation using a sparse coding and dictionary learning method. The proposed framework consists of two steps: classification and segmentation. The classification of the brain tumors is based on brain topology and texture. The segmentation is based on voxel values of the image data. Using K-SVD, two types of dictionaries are learned from the training data and their associated ground truth segmentation: feature dictionary and voxel-wise coupled dictionaries. The feature dictionary consists of global image features (topological and texture features). The coupled dictionaries consist of coupled information: gray scale voxel values of the training image data and their associated label voxel values of the ground truth segmentation of the training data. For quantitative evaluation, the proposed framework is evaluated using different metrics. The segmentation results of the brain tumor segmentation (MICCAI-BraTS-2013) database are evaluated using five different metric scores, which are computed using the online evaluation tool provided by the BraTS-2013 challenge organizers. Experimental results demonstrate that the proposed approach achieves an accurate brain tumor classification and segmentation and outperforms the state-of-the-art methods.

Saliency Detection Based on Multi-Scale Superpixel and Dictionary Learning

In recent years, saliency detection has been gaining increasing attention since it could significantly boost many content-based multimedia applications. In this paper, we propose a visual saliency detection algorithm based on multi-scale superpixel and dictionary learning . Firstly, in each scale space, we extract the boundaries as the training samples to learn a dictionary through sparse coding and dictionary learning methods. Then, according to reconstruction error of each superpixel, the saliency map is generated for each scale of superpixel. Finally, some saliency maps from different scale spaces are fused together to generate the final saliency map. The experimental results show that the proposed algorithm can highlight the salient regions uniformly and performs better compared with the other five methods.

A Multichannel Gray Level Co-Occurrence Matrix for Multi/Hyperspectral Image Texture Representation

This study proposes a novel method for multichannel image gray level co-occurrence matrix (GLCM) texture representation. It is well known that the standard procedure for the automatic extraction of GLCM textures is based on a mono-spectral image. In real applications, however, the GLCM texture feature extraction always refers to multi/hyperspectral images. The widely used strategy to deal with this issue is to calculate the GLCM from the first principal component or the panchromatic band, which do not include all the useful information. Accordingly, in this study, we propose to represent the multichannel textures for multi/hyperspectral imagery by the use of: (1) clustering algorithms; and (2) sparse representation, respectively. In this way, the multi/hyperspectral images can be described using a series of quantized codes or dictionaries, which are more suitable for multichannel texture representation than the traditional methods. Specifically, K-means and fuzzy c-means methods are adopted to generate the codes of an image from the clustering point of view, while a sparse dictionary learning method based on two coding rules is proposed to produce the texture primitives. The proposed multichannel GLCM textural extraction methods were evaluated with four multi/hyperspectral datasets: GeoEye-1 and QuickBird multispectral images of the city of Wuhan, the well-known AVIRIS hyperspectral dataset from the Indian Pines test site, and the HYDICE airborne hyperspectral dataset from the Washington DC Mall. The results show that both the clustering-based and sparsity-based GLCM textures outperform the traditional method (extraction based on the first principal component) in terms of classification accuracies in all the experiments.

Deformable segmentation of 3D MR prostate images via distributed discriminative dictionary and ensemble learning.

Automatic prostate segmentation from MR images is an important task in various clinical applications such as prostate cancer staging and MR-guided radiotherapy planning. However, the large appearance and shape variations of the prostate in MR images make the segmentation problem difficult to solve. Traditional Active Shape/Appearance Model (ASM/AAM) has limited accuracy on this problem, since its basic assumption, i.e., both shape and appearance of the targeted organ follow Gaussian distributions, is invalid in prostate MR images. To this end, the authors propose a sparse dictionary learning method to model the image appearance in a nonparametric fashion and further integrate the appearance model into a deformable segmentation framework for prostate MR segmentation. To drive the deformable model for prostate segmentation, the authors propose nonparametric appearance and shape models. The nonparametric appearance model is based on a novel dictionary learning method, namely distributed discriminative dictionary (DDD) learning, which is able to capture fine distinctions in image appearance. To increase the differential power of traditional dictionary-based classification methods, the authors' DDD learning approach takes three strategies. First, two dictionaries for prostate and nonprostate tissues are built, respectively, using the discriminative features obtained from minimum redundancy maximum relevance feature selection. Second, linear discriminant analysis is employed as a linear classifier to boost the optimal separation between prostate and nonprostate tissues, based on the representation residuals from sparse representation. Third, to enhance the robustness of the authors' classification method, multiple local dictionaries are learned for local regions along the prostate boundary (each with small appearance variations), instead of learning one global classifier for the entire prostate. These discriminative dictionaries are located on different patches of the prostate surface and trained to adaptively capture the appearance in different prostate zones, thus achieving better local tissue differentiation. For each local region, multiple classifiers are trained based on the randomly selected samples and finally assembled by a specific fusion method. In addition to this nonparametric appearance model, a prostate shape model is learned from the shape statistics using a novel approach, sparse shape composition, which can model nonGaussian distributions of shape variation and regularize the 3D mesh deformation by constraining it within the observed shape subspace. The proposed method has been evaluated on two datasets consisting of T2-weighted MR prostate images. For the first (internal) dataset, the classification effectiveness of the authors' improved dictionary learning has been validated by comparing it with three other variants of traditional dictionary learning methods. The experimental results show that the authors' method yields a Dice Ratio of 89.1% compared to the manual segmentation, which is more accurate than the three state-of-the-art MR prostate segmentation methods under comparison. For the second dataset, the MICCAI 2012 challenge dataset, the authors' proposed method yields a Dice Ratio of 87.4%, which also achieves better segmentation accuracy than other methods under comparison. A new magnetic resonance image prostate segmentation method is proposed based on the combination of deformable model and dictionary learning methods, which achieves more accurate segmentation performance on prostate T2 MR images.

Automatic Ki-67 Counting Using Robust Cell Detection and Online Dictionary Learning

Ki-67 proliferation index is a valid and important biomarker to gauge neuroendocrine tumor (NET) cell progression within the gastrointestinal tract and pancreas. Automatic Ki-67 assessment is very challenging due to complex variations of cell characteristics. In this paper, we propose an integrated learning-based framework for accurate automatic Ki-67 counting for NET. The main contributions of our method are: 1) A robust cell counting and boundary delineation algorithm that is designed to localize both tumor and nontumor cells. 2) A novel online sparse dictionary learning method to select a set of representative training samples. 3) An automated framework that is used to differentiate tumor from nontumor cells (such as lymphocytes) and immunopositive from immunonegative tumor cells for the assessment of Ki-67 proliferation index. The proposed method has been extensively tested using 46 NET cases. The performance is compared with pathologists' manual annotations. The automatic Ki-67 counting is quite accurate compared with pathologists' manual annotations. This is much more accurate than existing methods.