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109
Image deblurring and superresolution by adaptive sparse domain selection and adaptive regularization
 IEEE Trans. Image Process
, 2011
"... Abstract—As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of thenorm optimization techniques and the fact that natural images are intrinsically ..."
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Cited by 56 (11 self)
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Abstract—As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of thenorm optimization techniques and the fact that natural images are intrinsically sparse in some domains. The image restoration quality largely depends on whether the employed sparse domain can represent well the underlying image. Considering that the contents can vary significantly across different images or different patches in a single image, we propose to learn various sets of bases from a precollected dataset of example image patches, and then, for a given patch to be processed, one set of bases are adaptively selected to characterize the local sparse domain. We further introduce two adaptive regularization terms into the sparse representation framework. First, a set of autoregressive (AR) models are learned from the dataset of example image patches. The best fitted AR models to a given patch are adaptively selected to regularize the image local structures. Second, the image nonlocal selfsimilarity is introduced as another regularization term. In addition, the sparsity regularization parameter is adaptively estimated for better image restoration performance. Extensive experiments on image deblurring and superresolution validate that by using adaptive sparse domain selection and adaptive regularization, the proposed method achieves much better results than many stateoftheart algorithms in terms of both PSNR and visual perception. Index Terms—Deblurring, image restoration (IR), regularization, sparse representation, superresolution. I.
Hierarchical Matching Pursuit for Image Classification: Architecture and Fast Algorithms
"... Extracting good representations from images is essential for many computer vision tasks. In this paper, we propose hierarchical matching pursuit (HMP), which builds a feature hierarchy layerbylayer using an efficient matching pursuit encoder. It includes three modules: batch (tree) orthogonal matc ..."
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Cited by 39 (11 self)
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Extracting good representations from images is essential for many computer vision tasks. In this paper, we propose hierarchical matching pursuit (HMP), which builds a feature hierarchy layerbylayer using an efficient matching pursuit encoder. It includes three modules: batch (tree) orthogonal matching pursuit, spatial pyramid max pooling, and contrast normalization. We investigate the architecture of HMP, and show that all three components are critical for good performance. To speed up the orthogonal matching pursuit, we propose a batch tree orthogonal matching pursuit that is particularly suitable to encode a large number of observations that share the same large dictionary. HMP is scalable and can efficiently handle fullsize images. In addition, HMP enables linear support vector machines (SVM) to match the performance of nonlinear SVM while being scalable to large datasets. We compare HMP with many stateoftheart algorithms including convolutional deep belief networks, SIFT based single layer sparse coding, and kernel based feature learning. HMP consistently yields superior accuracy on three types of image classification problems: object recognition (Caltech101), scene recognition (MITScene), and static event recognition (UIUCSports). 1
Exact Recovery of SparselyUsed Dictionaries
 25TH ANNUAL CONFERENCE ON LEARNING THEORY
, 2012
"... We consider the problem of learning sparsely used dictionaries with an arbitrary square dictionary and a random, sparse coefficient matrix. We prove that O(n log n) samples are sufficient to uniquely determine the coefficient matrix. Based on this proof, we design a polynomialtime algorithm, called ..."
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Cited by 37 (2 self)
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We consider the problem of learning sparsely used dictionaries with an arbitrary square dictionary and a random, sparse coefficient matrix. We prove that O(n log n) samples are sufficient to uniquely determine the coefficient matrix. Based on this proof, we design a polynomialtime algorithm, called Exact Recovery of SparselyUsed Dictionaries (ERSpUD), and prove that it probably recovers the dictionary and coefficient matrix when the coefficient matrix is sufficiently sparse. Simulation results show that ERSpUD reveals the true dictionary as well as the coefficients with probability higher than many stateoftheart algorithms.
Nonlocally Centralized Sparse Representation for Image Restoration
, 2011
"... The sparse representation models code an image patch as a linear combination of a few atoms chosen out from an overcomplete dictionary, and they have shown promising results in various image restoration applications. However, due to the degradation of the observed image (e.g., noisy, blurred and/o ..."
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Cited by 25 (8 self)
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The sparse representation models code an image patch as a linear combination of a few atoms chosen out from an overcomplete dictionary, and they have shown promising results in various image restoration applications. However, due to the degradation of the observed image (e.g., noisy, blurred and/or downsampled), the sparse representations by conventional models may not be accurate enough for a faithful reconstruction of the original image. To improve the performance of sparse representation based image restoration, in this paper the concept of sparse coding noise is introduced, and the goal of image restoration turns to how to suppress the sparse coding noise. To this end, we exploit the image nonlocal selfsimilarity to obtain good estimates of the sparse coding coefficients of the original image, and then centralize the sparse coding coefficients of the observed image to those estimates. The socalled nonlocally centralized sparse representation (NCSR) model is as simple as the standard sparse representation model, while our extensive experiments on various types of image restoration problems, including denoising, deblurring and superresolution, validate the generality and stateoftheart performance of the proposed NCSR algorithm.
Analysis KSVD: A DictionaryLearning Algorithm for the Analysis Sparse Model
, 2012
"... The synthesisbased sparse representation model for signals has drawn considerable interest in the past decade. Such a model assumes that the signal of interest can be decomposed as a linear combination of a few atoms from a given dictionary. In this paper we concentrate on an alternative, analysis ..."
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Cited by 21 (6 self)
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The synthesisbased sparse representation model for signals has drawn considerable interest in the past decade. Such a model assumes that the signal of interest can be decomposed as a linear combination of a few atoms from a given dictionary. In this paper we concentrate on an alternative, analysisbased model, where an analysis operator – hereafter referred to as the analysis dictionary – multiplies the signal, leading to a sparse outcome. Our goal is to learn the analysis dictionary from a set of examples. The approach taken is parallel and similar to the one adopted by the KSVD algorithm that serves the corresponding problem in the synthesis model. We present the development of the algorithm steps: This includes tailored pursuit algorithms – the Backward Greedy and the Optimized Backward Greedy algorithms, and a penalty function that defines the objective for the dictionary update stage. We demonstrate the effectiveness of the proposed dictionary learning in several experiments, treating synthetic data and real images, and showing a successful and meaningful recovery of the analysis dictionary.
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
, 2011
"... The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smoot ..."
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Cited by 21 (8 self)
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The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multiorientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to nonEuclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping “pictures”.
Domain Adaptive Dictionary Learning
"... Abstract. Many recent efforts have shown the effectiveness of dictionary learning methods in solving several computer vision problems. However, when designing dictionaries, training and testing domains may be different, due to different view points and illumination conditions. In this paper, we pres ..."
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Cited by 18 (9 self)
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Abstract. Many recent efforts have shown the effectiveness of dictionary learning methods in solving several computer vision problems. However, when designing dictionaries, training and testing domains may be different, due to different view points and illumination conditions. In this paper, we present a function learning framework for the task of transforming a dictionary learned from one visual domain to the other, while maintaining a domaininvariant sparse representation of a signal. Domain dictionaries are modeled by a linear or nonlinear parametric function. The dictionary function parameters and domaininvariant sparse codes are then jointly learned by solving an optimization problem. Experiments on real datasets demonstrate the effectiveness of our approach for applications such as face recognition, pose alignment and pose estimation. 1
Highresolution Hyperspectral Imaging via Matrix Factorization
"... Hyperspectral imaging is a promising tool for applications in geosensing, cultural heritage and beyond. However, compared to current RGB cameras, existing hyperspectral cameras are severely limited in spatial resolution. In this paper, we introduce a simple new technique for reconstructing a very hi ..."
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Cited by 15 (0 self)
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Hyperspectral imaging is a promising tool for applications in geosensing, cultural heritage and beyond. However, compared to current RGB cameras, existing hyperspectral cameras are severely limited in spatial resolution. In this paper, we introduce a simple new technique for reconstructing a very highresolution hyperspectral image from two readily obtained measurements: A lowerresolution hyperspectral image and a highresolution RGB image. Our approach is divided into two stages: We first apply an unmixing algorithm to the hyperspectral input, to estimate a basis representing reflectance spectra. We then use this representation in conjunction with the RGB input to produce the desired result. Our approach to unmixing is motivated by the spatial sparsity of the hyperspectral input, and casts the unmixing problem as the search for a factorization of the input into a basis and a set of maximally sparse coefficients. Experiments show that this simple approach performs reasonably well on both simulations and real data examples. 1.
Simultaneous codeword optimization (SimCO) for dictionary update and learning
 IEEE Trans. Signal Process
, 2012
"... Abstract—We consider the datadriven dictionary learning problem. The goal is to seek an overcomplete dictionary from which every training signal can be best approximated by a linear combination of only a few codewords. This task is often achieved by iteratively executing two operations: sparse cod ..."
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Cited by 13 (7 self)
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Abstract—We consider the datadriven dictionary learning problem. The goal is to seek an overcomplete dictionary from which every training signal can be best approximated by a linear combination of only a few codewords. This task is often achieved by iteratively executing two operations: sparse coding and dictionary update. In the literature, there are two benchmark mechanisms to update a dictionary. The first approach, for example the MOD algorithm, is characterized by searching for the optimal codewords while fixing the sparse coefficients. In the second approach, represented by the KSVD method, one codeword and the related sparse coefficients are simultaneously updated while all other codewords and coefficients remain unchanged. We propose a novel framework that generalizes the aforementioned two methods. The unique feature of our approach is that one can update an arbitrary set of codewords and the corresponding sparse coefficients simultaneously: when sparse coefficients are fixed, the underlying optimization problem is the same as that in the MOD algorithm; when only one codeword is selected for update, it can be proved that the proposed algorithm is equivalent to the KSVD method; and more importantly, our method allows to update all codewords and all sparse coefficients simultaneously, hence the term simultaneously codeword optimization (SimCO). Under the proposed framework, we design two algorithms, namely the primitive and regularized SimCO. Simulations demonstrate that our approach excels the benchmark KSVD in terms of both learning performance and running speed. I.
Constrained Overcomplete Analysis Operator Learning for Cosparse Signal Modelling
"... We consider the problem of learning a lowdimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of thetraining samples using sparsesynthesis coefficients. This famous sparse model has a less ..."
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Cited by 12 (1 self)
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We consider the problem of learning a lowdimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of thetraining samples using sparsesynthesis coefficients. This famous sparse model has a less well known counterpart, in analysis form, called the cosparse analysis model. In this new model, signals are characterised by their parsimony in a transformed domain using an overcomplete (linear) analysis operator. We propose to learn an analysis operator from a training corpus using a constrained optimisation framework based on L1 optimisation. The reason for introducing a constraint in the optimisation framework is to exclude trivial solutions. Although there is no final answer here for which constraint is the most relevant constraint, we investigate some conventional constraints in the model adaptation field and use the uniformly normalised tight frame (UNTF) for this purpose. We then derive a practical learning algorithm, based on projected subgradients and DouglasRachford splitting technique, and demonstrate its ability to robustly recover a ground truth analysis operator, when provided with a clean training set, of sufficient size. We also find an analysis operator for images, using some noisy cosparse signals, which is indeed a more realistic experiment. As the derived optimisation problem is not a convex program, we often find a local minimum using such variational methods. For two different settings, we provide preliminary theoretical support for the wellposedness of the learning problem, which can be practically used to test the local identifiability conditions of learnt operators.