Showing papers on "Sparse approximation published in 2017"

On Compressing Deep Models by Low Rank and Sparse Decomposition

Abstract: Deep compression refers to removing the redundancy of parameters and feature maps for deep learning models. Low-rank approximation and pruning for sparse structures play a vital role in many compression works. However, weight filters tend to be both low-rank and sparse. Neglecting either part of these structure information in previous methods results in iteratively retraining, compromising accuracy, and low compression rates. Here we propose a unified framework integrating the low-rank and sparse decomposition of weight matrices with the feature map reconstructions. Our model includes methods like pruning connections as special cases, and is optimized by a fast SVD-free algorithm. It has been theoretically proven that, with a small sample, due to its generalizability, our model can well reconstruct the feature maps on both training and test data, which results in less compromising accuracy prior to the subsequent retraining. With such a warm start to retrain, the compression method always possesses several merits: (a) higher compression rates, (b) little loss of accuracy, and (c) fewer rounds to compress deep models. The experimental results on several popular models such as AlexNet, VGG-16, and GoogLeNet show that our model can significantly reduce the parameters for both convolutional and fully-connected layers. As a result, our model reduces the size of VGG-16 by 15×, better than other recent compression methods that use a single strategy.

Robust Joint Graph Sparse Coding for Unsupervised Spectral Feature Selection

Abstract: In this paper, we propose a new unsupervised spectral feature selection model by embedding a graph regularizer into the framework of joint sparse regression for preserving the local structures of data. To do this, we first extract the bases of training data by previous dictionary learning methods and, then, map original data into the basis space to generate their new representations, by proposing a novel joint graph sparse coding (JGSC) model. In JGSC, we first formulate its objective function by simultaneously taking subspace learning and joint sparse regression into account, then, design a new optimization solution to solve the resulting objective function, and further prove the convergence of the proposed solution. Furthermore, we extend JGSC to a robust JGSC (RJGSC) via replacing the least square loss function with a robust loss function, for achieving the same goals and also avoiding the impact of outliers. Finally, experimental results on real data sets showed that both JGSC and RJGSC outperformed the state-of-the-art algorithms in terms of ${k}$ -nearest neighbor classification performance.

Submanifold Sparse Convolutional Networks

Abstract: Convolutional network are the de-facto standard for analysing spatio-temporal data such as images, videos, 3D shapes, etc. Whilst some of this data is naturally dense (for instance, photos), many other data sources are inherently sparse. Examples include pen-strokes forming on a piece of paper, or (colored) 3D point clouds that were obtained using a LiDAR scanner or RGB-D camera. Standard "dense" implementations of convolutional networks are very inefficient when applied on such sparse data. We introduce a sparse convolutional operation tailored to processing sparse data that differs from prior work on sparse convolutional networks in that it operates strictly on submanifolds, rather than "dilating" the observation with every layer in the network. Our empirical analysis of the resulting submanifold sparse convolutional networks shows that they perform on par with state-of-the-art methods whilst requiring substantially less computation.

Sparse Regularization via Convex Analysis

Abstract: Sparse approximate solutions to linear equations are classically obtained via L1 norm regularized least squares, but this method often underestimates the true solution As an alternative to the L1 norm, this paper proposes a class of nonconvex penalty functions that maintain the convexity of the least squares cost function to be minimized, and avoids the systematic underestimation characteristic of L1 norm regularization The proposed penalty function is a multivariate generalization of the minimax-concave penalty It is defined in terms of a new multivariate generalization of the Huber function, which in turn is defined via infimal convolution The proposed sparse-regularized least squares cost function can be minimized by proximal algorithms comprising simple computations

Complete Dictionary Recovery Over the Sphere I: Overview and the Geometric Picture

Abstract: We consider the problem of recovering a complete (i.e., square and invertible) matrix $ A_{0}$ , from $ Y \in \mathbb R ^{n \times p}$ with $ Y = A_{0} X_{0}$ , provided $ X_{0}$ is sufficiently sparse. This recovery problem is central to theoretical understanding of dictionary learning, which seeks a sparse representation for a collection of input signals and finds numerous applications in modern signal processing and machine learning. We give the first efficient algorithm that provably recovers $ A_{0}$ when $ X_{0}$ has $O \left ({ n }\right )$ nonzeros per column, under suitable probability model for $ X_{0}$ . In contrast, prior results based on efficient algorithms either only guarantee recovery when $ X_{0}$ has $O(\sqrt {n})$ zeros per column, or require multiple rounds of semidefinite programming relaxation to work when $ X_{0}$ has $O(n)$ nonzeros per column. Our algorithmic pipeline centers around solving a certain nonconvex optimization problem with a spherical constraint. In this paper, we provide a geometric characterization of the objective landscape. In particular, we show that the problem is highly structured with high probability: 1) there are no “spurious” local minimizers and 2) around all saddle points the objective has a negative directional curvature. This distinctive structure makes the problem amenable to efficient optimization algorithms. In a companion paper, we design a second-order trust-region algorithm over the sphere that provably converges to a local minimizer from arbitrary initializations, despite the presence of saddle points.

Convolutional neural networks analyzed via convolutional sparse coding

Abstract: Convolutional neural networks (CNN) have led to many state-of-the-art results spanning through various fields. However, a clear and profound theoretical understanding of the forward pass, the core algorithm of CNN, is still lacking. In parallel, within the wide field of sparse approximation, Convolutional Sparse Coding (CSC) has gained increasing attention in recent years. A theoretical study of this model was recently conducted, establishing it as a reliable and stable alternative to the commonly practiced patch-based processing. Herein, we propose a novel multi-layer model, ML-CSC, in which signals are assumed to emerge from a cascade of CSC layers. This is shown to be tightly connected to CNN, so much so that the forward pass of the CNN is in fact the thresholding pursuit serving the ML-CSC model. This connection brings a fresh view to CNN, as we are able to attribute to this architecture theoretical claims such as uniqueness of the representations throughout the network, and their stable estimation, all guaranteed under simple local sparsity conditions. Lastly, identifying the weaknesses in the above pursuit scheme, we propose an alternative to the forward pass, which is connected to deconvolutional and recurrent networks, and also has better theoretical guarantees.

Transferred Deep Learning for Anomaly Detection in Hyperspectral Imagery

Abstract: In this letter, a novel anomaly detection framework with transferred deep convolutional neural network (CNN) is proposed. The framework is designed by considering the following facts: 1) a reference data with labeled samples are utilized, because no prior information is available about the image scene for anomaly detection and 2) pixel pairs are generated to enlarge the sample size, since the advantage of CNN can be realized only if the number of training samples is sufficient. A multilayer CNN is trained by using difference between pixel pairs generated from the reference image scene. Then, for each pixel in the image for anomaly detection, difference between pixel pairs, constructed by combining the center pixel and its surrounding pixels, is classified by the trained CNN with the result of similarity measurement. The detection output is simply generated by averaging these similarity scores. Experimental performance demonstrates that the proposed algorithm outperforms the classic Reed-Xiaoli and the state-of-the-art representation-based detectors, such as sparse representation-based detector (SRD) and collaborative representation-based detector.

Robust Object Tracking via Key Patch Sparse Representation

Abstract: Many conventional computer vision object tracking methods are sensitive to partial occlusion and background clutter. This is because the partial occlusion or little background information may exist in the bounding box, which tends to cause the drift. To this end, in this paper, we propose a robust tracker based on key patch sparse representation (KPSR) to reduce the disturbance of partial occlusion or unavoidable background information. Specifically, KPSR first uses patch sparse representations to get the patch score of each patch. Second, KPSR proposes a selection criterion of key patch to judge the patches within the bounding box and select the key patch according to its location and occlusion case. Third, KPSR designs the corresponding contribution factor for the sampled patches to emphasize the contribution of the selected key patches. Comparing the KPSR with eight other contemporary tracking methods on 13 benchmark video data sets, the experimental results show that the KPSR tracker outperforms classical or state-of-the-art tracking methods in the presence of partial occlusion, background clutter, and illumination change.

Semi-Supervised Sparse Representation Based Classification for Face Recognition With Insufficient Labeled Samples

Abstract: This paper addresses the problem of face recognition when there is only few, or even only a single, labeled examples of the face that we wish to recognize. Moreover, these examples are typically corrupted by nuisance variables, both linear (i.e., additive nuisance variables, such as bad lighting and wearing of glasses) and non-linear (i.e., non-additive pixel-wise nuisance variables, such as expression changes). The small number of labeled examples means that it is hard to remove these nuisance variables between the training and testing faces to obtain good recognition performance. To address the problem, we propose a method called semi-supervised sparse representation-based classification. This is based on recent work on sparsity, where faces are represented in terms of two dictionaries: a gallery dictionary consisting of one or more examples of each person, and a variation dictionary representing linear nuisance variables (e.g., different lighting conditions and different glasses). The main idea is that: 1) we use the variation dictionary to characterize the linear nuisance variables via the sparsity framework and 2) prototype face images are estimated as a gallery dictionary via a Gaussian mixture model, with mixed labeled and unlabeled samples in a semi-supervised manner, to deal with the non-linear nuisance variations between labeled and unlabeled samples. We have done experiments with insufficient labeled samples, even when there is only a single labeled sample per person. Our results on the AR, Multi-PIE, CAS-PEAL, and LFW databases demonstrate that the proposed method is able to deliver significantly improved performance over existing methods.

Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework

Abstract: Subspace clustering refers to the problem of segmenting data drawn from a union of subspaces. State-of-the-art approaches for solving this problem follow a two-stage approach. In the first step, an affinity matrix is learned from the data using sparse or low-rank minimization techniques. In the second step, the segmentation is found by applying spectral clustering to this affinity. While this approach has led to the state-of-the-art results in many applications, it is suboptimal, because it does not exploit the fact that the affinity and the segmentation depend on each other. In this paper, we propose a joint optimization framework — Structured Sparse Subspace Clustering (S3C) — for learning both the affinity and the segmentation. The proposed S3C framework is based on expressing each data point as a structured sparse linear combination of all other data points, where the structure is induced by a norm that depends on the unknown segmentation. Moreover, we extend the proposed S3C framework into Constrained S3C (CS3C) in which available partial side-information is incorporated into the stage of learning the affinity. We show that both the structured sparse representation and the segmentation can be found via a combination of an alternating direction method of multipliers with spectral clustering. Experiments on a synthetic data set, the Extended Yale B face data set, the Hopkins 155 motion segmentation database, and three cancer data sets demonstrate the effectiveness of our approach.

Joint Convolutional Analysis and Synthesis Sparse Representation for Single Image Layer Separation

Abstract: Analysis sparse representation (ASR) and synthesis sparse representation (SSR) are two representative approaches for sparsity-based image modeling. An image is described mainly by the non-zero coefficients in SSR, while is mainly characterized by the indices of zeros in ASR. To exploit the complementary representation mechanisms of ASR and SSR, we integrate the two models and propose a joint convolutional analysis and synthesis (JCAS) sparse representation model. The convolutional implementation is adopted to more effectively exploit the image global information. In JCAS, a single image is decomposed into two layers, one is approximated by ASR to represent image large-scale structures, and the other by SSR to represent image fine-scale textures. The synthesis dictionary is adaptively learned in JCAS to describe the texture patterns for different single image layer separation tasks. We evaluate the proposed JCAS model on a variety of applications, including rain streak removal, high dynamic range image tone mapping, etc. The results show that our JCAS method outperforms state-of-the-arts in these applications in terms of both quantitative measure and visual perception quality.

A BaSiC tool for background and shading correction of optical microscopy images.

Abstract: Quantitative analysis of bioimaging data is often skewed by both shading in space and background variation in time. We introduce BaSiC, an image correction method based on low-rank and sparse decomposition which solves both issues. In comparison to existing shading correction tools, BaSiC achieves high-accuracy with significantly fewer input images, works for diverse imaging conditions and is robust against artefacts. Moreover, it can correct temporal drift in time-lapse microscopy data and thus improve continuous single-cell quantification. BaSiC requires no manual parameter setting and is available as a Fiji/ImageJ plugin.

Sparse Representation for 3D Shape Estimation: A Convex Relaxation Approach

Abstract: We investigate the problem of estimating the 3D shape of an object defined by a set of 3D landmarks, given their 2D correspondences in a single image. A successful approach to alleviating the reconstruction ambiguity is the 3D deformable shape model and a sparse representation is often used to capture complex shape variability. But the model inference is still challenging due to the nonconvexity in the joint optimization of shape and viewpoint. In contrast to prior work that relies on an alternating scheme whose solution depends on initialization, we propose a convex approach to addressing this challenge and develop an efficient algorithm to solve the proposed convex program. We further propose a robust model to handle gross errors in the 2D correspondences. We demonstrate the exact recovery property of the proposed method, the advantage compared to several nonconvex baselines and the applicability to recover 3D human poses and car models from single images.

A New Discriminative Sparse Representation Method for Robust Face Recognition via $l_{2}$ Regularization

Abstract: Sparse representation has shown an attractive performance in a number of applications. However, the available sparse representation methods still suffer from some problems, and it is necessary to design more efficient methods. Particularly, to design a computationally inexpensive, easily solvable, and robust sparse representation method is a significant task. In this paper, we explore the issue of designing the simple, robust, and powerfully efficient sparse representation methods for image classification. The contributions of this paper are as follows. First, a novel discriminative sparse representation method is proposed and its noticeable performance in image classification is demonstrated by the experimental results. More importantly, the proposed method outperforms the existing state-of-the-art sparse representation methods. Second, the proposed method is not only very computationally efficient but also has an intuitive and easily understandable idea. It exploits a simple algorithm to obtain a closed-form solution and discriminative representation of the test sample. Third, the feasibility, computational efficiency, and remarkable classification accuracy of the proposed $l_{2}$ regularization-based representation are comprehensively shown by extensive experiments and analysis. The code of the proposed method is available at http://www.yongxu.org/lunwen.html .

Sparse model selection via integral terms.

Abstract: Model selection and parameter estimation are important for the effective integration of experimental data, scientific theory, and precise simulations. In this work, we develop a learning approach for the selection and identification of a dynamical system directly from noisy data. The learning is performed by extracting a small subset of important features from an overdetermined set of possible features using a nonconvex sparse regression model. The sparse regression model is constructed to fit the noisy data to the trajectory of the dynamical system while using the smallest number of active terms. Computational experiments detail the model's stability, robustness to noise, and recovery accuracy. Examples include nonlinear equations, population dynamics, chaotic systems, and fast-slow systems.

Training Sparse Neural Networks

Abstract: The emergence of Deep neural networks has seen human-level performance on large scale computer vision tasks such as image classification. However these deep networks typically contain large amount of parameters due to dense matrix multiplications and convolutions. As a result, these architectures are highly memory intensive, making them less suitable for embedded vision applications. Sparse Computations are known to be much more memory efficient. In this work, we train and build neural networks which implicitly use sparse computations. We introduce additional gate variables to perform parameter selection and show that this is equivalent to using a spike-and-slab prior. We experimentally validate our method on both small and large networks which result in highly sparse neural network models.

Fault Diagnosis for a Wind Turbine Generator Bearing via Sparse Representation and Shift-Invariant K-SVD

Abstract: It is always a primary challenge in fault diagnosis of a wind turbine generator to extract fault character information under strong noise and nonstationary condition. As a novel signal processing method, sparse representation shows excellent performance in time–frequency analysis and feature extraction. However, its result is directly influenced by dictionary, whose atoms should be as similar with signal's inner structure as possible. Due to the variability of operation environment and physical structure in industrial systems, the patterns of impulse signals are changing over time, which makes creating a proper dictionary even harder. To solve the problem, a novel data-driven fault diagnosis method based on sparse representation and shift-invariant dictionary learning is proposed. The impulse signals at different locations with the same characteristic can be represented by only one atom through shift operation. Then, the shift-invariant dictionary is generated by taking all the possible shifts of a few short atoms and, consequently, is more applicable to represent long signals that in the same pattern appear periodically. Based on the learnt shift-invariant dictionary, the coefficients obtained can be sparser, with the extracted impulse signal being closer to the real signal. Finally, the time–frequency representation of the impulse component is obtained with consideration of both the Wigner–Ville distribution of every atom and the corresponding sparse coefficient. The excellent performance of different fault diagnoses in a fault simulator and a wind turbine proves the effectiveness and robustness of the proposed method. Meanwhile, the comparison with the state-of-the-art method is illustrated, which highlights the superiority of the proposed method.

Joint Dictionary Learning for Multispectral Change Detection

Abstract: Change detection is one of the most important applications of remote sensing technology. It is a challenging task due to the obvious variations in the radiometric value of spectral signature and the limited capability of utilizing spectral information. In this paper, an improved sparse coding method for change detection is proposed. The intuition of the proposed method is that unchanged pixels in different images can be well reconstructed by the joint dictionary, which corresponds to knowledge of unchanged pixels, while changed pixels cannot. First, a query image pair is projected onto the joint dictionary to constitute the knowledge of unchanged pixels. Then reconstruction error is obtained to discriminate between the changed and unchanged pixels in the different images. To select the proper thresholds for determining changed regions, an automatic threshold selection strategy is presented by minimizing the reconstruction errors of the changed pixels. Adequate experiments on multispectral data have been tested, and the experimental results compared with the state-of-the-art methods prove the superiority of the proposed method. Contributions of the proposed method can be summarized as follows: 1) joint dictionary learning is proposed to explore the intrinsic information of different images for change detection. In this case, change detection can be transformed as a sparse representation problem. To the authors’ knowledge, few publications utilize joint learning dictionary in change detection; 2) an automatic threshold selection strategy is presented, which minimizes the reconstruction errors of the changed pixels without the prior assumption of the spectral signature. As a result, the threshold value provided by the proposed method can adapt to different data due to the characteristic of joint dictionary learning; and 3) the proposed method makes no prior assumption of the modeling and the handling of the spectral signature, which can be adapted to different data.

Sparse Representation-Based Open Set Recognition

Abstract: We propose a generalized Sparse Representation-based Classification (SRC) algorithm for open set recognition where not all classes presented during testing are known during training. The SRC algorithm uses class reconstruction errors for classification. As most of the discriminative information for open set recognition is hidden in the tail part of the matched and sum of non-matched reconstruction error distributions, we model the tail of those two error distributions using the statistical Extreme Value Theory (EVT). Then we simplify the open set recognition problem into a set of hypothesis testing problems. The confidence scores corresponding to the tail distributions of a novel test sample are then fused to determine its identity. The effectiveness of the proposed method is demonstrated using four publicly available image and object classification datasets and it is shown that this method can perform significantly better than many competitive open set recognition algorithms.

Complete Dictionary Recovery Over the Sphere II: Recovery by Riemannian Trust-Region Method

Abstract: We consider the problem of recovering a complete (i.e., square and invertible) matrix $ A_{0}$ , from $ Y \in \mathbb R ^{n \times p}$ with $Y = \boldsymbol A_{0} X_{0}$ , provided $ X_{0}$ is sufficiently sparse. This recovery problem is central to theoretical understanding of dictionary learning, which seeks a sparse representation for a collection of input signals and finds numerous applications in modern signal processing and machine learning. We give the first efficient algorithm that provably recovers $ A_{0}$ when $ X_{0}$ has $O \left ({ n }\right )$ nonzeros per column, under suitable probability model for $ X_{0}$ . Our algorithmic pipeline centers around solving a certain nonconvex optimization problem with a spherical constraint, and hence is naturally phrased in the language of manifold optimization. In a companion paper, we have showed that with high probability, our nonconvex formulation has no “spurious” local minimizers and around any saddle point, the objective function has a negative directional curvature. In this paper, we take advantage of the particular geometric structure and describe a Riemannian trust region algorithm that provably converges to a local minimizer with from arbitrary initializations. Such minimizers give excellent approximations to the rows of $ X_{0}$ . The rows are then recovered by a linear programming rounding and deflation.

Hyperspectral Image Classification via Multiple-Feature-Based Adaptive Sparse Representation

Abstract: A multiple-feature-based adaptive sparse representation (MFASR) method is proposed for the classification of hyperspectral images (HSIs). The proposed method mainly includes the following steps. First, four different features are separately extracted from the original HSI and they reflect different kinds of spectral and spatial information. Second, for each pixel, a shape adaptive (SA) spatial region is extracted. Third, an adaptive sparse representation algorithm is introduced to obtain the sparse coefficients for the multiple-feature matrix set of pixels in each SA region. Finally, these obtained coefficients are jointly used to determine the class label of each test pixel. Experimental results demonstrated that the proposed MFASR method can outperform several well-known classifiers in terms of both qualitative and quantitative results.

Two-stage plant species recognition by local mean clustering and Weighted sparse representation classification

Abstract: Aiming at the difficult problem of plant leaf recognition on the large-scale database, a two-stage local similarity based classification learning (LSCL) method is proposed by combining local mean-based clustering (LMC) method and local sparse representation based classification (SRC) (LWSRC). In the first stage, LMC is applied to coarsely classifying the test sample. k nearest neighbors of the test sample, as a neighbor subset, is selected from each training class, then the local geometric center of each class is calculated. S candidate neighbor subsets of the test sample are determined with the first S smallest distances between the test sample and each local geometric center. In the second stage, LWSRC is proposed to approximately represent the test sample through a linear weighted sum of all $$k\times S$$ samples of the S candidate neighbor subsets. Experimental results on the leaf image database demonstrate that the proposed method not only has a high accuracy and low time cost, but also can be clearly interpreted.

Communication-efficient sparse regression

Abstract: We devise a communication-efficient approach to distributed sparse regression in the high-dimensional setting. The key idea is to average "debiased" or "desparsified" lasso estimators. We show the approach converges at the same rate as the lasso as long as the dataset is not split across too many machines, and consistently estimates the support under weaker conditions than the lasso. On the computational side, we propose a new parallel and computationally-efficient algorithm to compute the approximate inverse covariance required in the debiasing approach, when the dataset is split across samples. We further extend the approach to generalized linear models.

Noise Robust Face Image Super-Resolution Through Smooth Sparse Representation

Abstract: Face image super-resolution has attracted much attention in recent years. Many algorithms have been proposed. Among them, sparse representation (SR)-based face image super-resolution approaches are able to achieve competitive performance. However, these SR-based approaches only perform well under the condition that the input is noiseless or has small noise. When the input is corrupted by large noise, the reconstruction weights (or coefficients) of the input low-resolution (LR) patches using SR-based approaches will be seriously unstable, thus leading to poor reconstruction results. To this end, in this paper, we propose a novel SR-based face image super-resolution approach that incorporates smooth priors to enforce similar training patches having similar sparse coding coefficients. Specifically, we introduce the fused least absolute shrinkage and selection operator-based smooth constraint and locality-based smooth constraint to the least squares representation-based patch representation in order to obtain stable reconstruction weights, especially when the noise level of the input LR image is high. Experiments are carried out on the benchmark FEI face database and CMU+MIT face database. Visual and quantitative comparisons show that the proposed face image super-resolution method yields superior reconstruction results when the input LR face image is contaminated by strong noise.

Weighted Joint Sparse Representation for Removing Mixed Noise in Image

Abstract: Joint sparse representation (JSR) has shown great potential in various image processing and computer vision tasks. Nevertheless, the conventional JSR is fragile to outliers. In this paper, we propose a weighted JSR (WJSR) model to simultaneously encode a set of data samples that are drawn from the same subspace but corrupted with noise and outliers. Our model is desirable to exploit the common information shared by these data samples while reducing the influence of outliers. To solve the WJSR model, we further introduce a greedy algorithm called weighted simultaneous orthogonal matching pursuit to efficiently approximate the global optimal solution. Then, we apply the WJSR for mixed noise removal by jointly coding the grouped nonlocal similar image patches. The denoising performance is further improved by incorporating it with the global prior and the sparse errors into a unified framework. Experimental results show that our denoising method is superior to several state-of-the-art mixed noise removal methods.

Working Locally Thinking Globally: Theoretical Guarantees for Convolutional Sparse Coding

Abstract: The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used for modeling low dimensional patches due to the computational constraints it entails when deployed with learned dictionaries. A way around this problem has been recently proposed, adopting a convolutional sparse representation model. This approach assumes that the global dictionary is a concatenation of banded circulant matrices. While several works have presented algorithmic solutions to the global pursuit problem under this new model, very few truly-effective guarantees are known for the success of such methods. In this paper, we address the theoretical aspects of the convolutional sparse model providing the first meaningful answers to questions of uniqueness of solutions and success of pursuit algorithms, both greedy and convex relaxations, in ideal and noisy regimes. To this end, we generalize mathematical quantities, such as the $\ell _0$ norm, mutual coherence, Spark and restricted isometry property to their counterparts in the convolutional setting, intrinsically capturing local measures of the global model. On the algorithmic side, we demonstrate how to solve the global pursuit problem by using simple local processing, thus offering a first of its kind bridge between global modeling of signals and their patch-based local treatment.