Single-Pass K-SVD for Efficient Dictionary Learning

This work presents a video compression method based on sparse representation and dictionary learning algorithms. The proposed scheme achieves superb rate-distortion performance and decent subjective quality, compared to modern standards, especially at low bit-rates. Different from similar works, sparse representation is employed here for both intra-frame and block matching inter-frame motion information. Dividing video frames to reference and current frames, motion vectors and motion compensation residuals of current frames are estimated in regard to reference frames. The sparse codes of reference frames and motion compensation residuals are obtained using learned dictionaries, entropy-coded, and stored or sent to the receiver along with the coded motion field. In the receiver, after decoding the sparse codes and motion vectors, the reference frames and residuals are reconstructed employing the same learned dictionary and the current frames are recovered using the reference frames and motion fields. In the proposed scheme, the Iterative Least Square Dictionary Learning Algorithm (ILS-DLA) and K-SVD dictionary building methods are employed in the DCT domain. The compression rate and quality of the method based on the two dictionary learning algorithms are compared to each other and to H.264/AVC and HEVC modern standards. The results based on PSNR and SSIM criteria show that the proposed approach presents superior performance respect to H.264/AVC and even HEVC for higher bit-rates of QCIF video format, and the K-SVD learning algorithm performs slightly better than the ILS-DLA for the purpose.

This paper describes how to construct a probability map using sparse representation and dictionary learning to indicate the probability of each optic disk pixel of belonging to the optic cup. This probability map will be used in the future as input to a method for automatically detecting glaucoma from color fundus images. The probability map was obtained constructing a model (using the Bayes classifier) which takes into account texture information, by means of sparse representation and RLS-DLA dictionary learning technique, and intensity information. Several experiments on a private database are presented in this work. The results are compared with the segmentation made by specialists, highlighting the promising performance of this technique in difficult cases where the optic cup is barely visible.

An automatic segmentation method of hippo-campus for volume measurement in MR brain images by using sparse patch representation and discriminative dictionary learning is proposed in this paper, which can overcome the limitation of multi-atlas approaches that mostly rely on similarity between target image and atlases for more accurate segmentation. In the proposed method, atlases are registered to a target image, then patch-based features including intensity and gradient are extracted from registered atlases for a dictionary learning model, from which dictionaries and classifiers are learned simultaneously. The label for voxels in the target image is determined via solving sparse representation of target patch over learned dictionary. Performance of the proposed method is evaluated on 30 subjects from the public dataset CIND by cross validation. Qualitative and quantitative comparisons illustrate that the proposed method is competitive compared with state-of-the-art approaches based on multi-atlas.

Retinal blood vessels are considered as being interference on the retinal images for the task of detecting significant features of the most frequent eye diseases. If these blood vessel structures could be suppressed, it might lead to a more accurate segmentation of retinal lesions as well as a better extraction of textural features to be used for pathology detection. This work proposes, as a novelty, the use of sparse representations and dictionary learning techniques for retinal vessel inpainting. The dictionary learning algorithms used in this paper were the Recursive Least Square Dictionary Learning (RLS-DL), and Online Dictionary Learning (ODL). We tested the performance of the algorithm for grayscale and RGB images from the DRIVE public database, employing different neighbourhoods and sparseness factors. An average recovery error smaller than 0.022 was achieved. The results suggest that the use of sparse representations and dictionaries learned by RLS-DLA performs very well for inpainting of retinal blood vessels.

Dictionary learning is still a challenging problem in signal and image processing. In this paper, we propose an efficient block-structured incoherent dictionary learning algorithm for sparse representations of image signals. The constrained minimization of dictionary learning is achieved by iteratively alternating between sparse coding and dictionary update. Without relying on any prior knowledge of the group structure for the input data, we develop a two-stage clustering method that identifies the underlying block structure of the dictionary under certain restricted constraints. The two-stage clustering method mainly consists of affinity propagation and agglomerative hierarchical clustering. To meet the conditions of both the upper bound and the lower bound of the mutual coherence of dictionary atoms, we introduce a regularization term for the objective function to adjust the block coherence of the overcomplete dictionary. The experiments on synthetic data and real images demonstrate that the proposed dictionary learning algorithm has lower representation error, higher visual quality and better reconstructed results than most of the state-of-the-art methods.

In this paper, we present an automated system for robust biometric recognition based upon sparse representation and dictionary learning. In sparse representation, extracted features from the training data are used to develop a dictionary. Training data of real world applications are likely to be exposed to geometric transformations, which is a big challenge for designing of discriminative dictionaries. Classification is achieved by representing the extracted features of the test data as a linear combination of entries in the dictionary. We propose joint weighted dictionary learning and classifier training (JWDL-CT) approach which simultaneously learns from a set of training samples along with weight vectors that correspond to the atoms in the learnt dictionary. The components of the weight vector associated with an atom represent the relationship between the atom and each of the classes. The weight vectors and atoms are jointly obtained during the dictionary learning. In the proposed method, a constraint is imposed on the correlation between the atoms to decrease the similarity between these atoms. The proposed dictionary learning objective function enhances the class-discrimination capabilities of individual atoms that renders the designed dictionaries especially suitable for classification of query images with very sparse representation. Experiments conducted on the West Virginia University (WVU) and the University of Notre Dame (UND) datasets for ear recognition show that the proposed method outperforms other state-of-the-art classifiers.

[1] Sparse geologic dictionaries provide a novel approach for subsurface flow model representation and calibration. Learning sparse dictionaries from prior training data sets is an effective approach to describe complex geologic connectivity patterns in subsurface imaging applications. However, the computational cost of sparse learning algorithms becomes prohibitive for large models. Performing the sparse dictionary learning process on smaller image patches (segments) provides a simple approach to address this problem in image processing applications. However, in underdetermined subsurface flow model calibration inverse problems, reconstruction of a segmented image can introduce significant structural distortion and discontinuity at the boundaries of the segments. This paper proposes an alternative sparse learning approach where the sparse dictionaries are learned from low-rank representations of the large-scale training data set in spectral domains (e.g., frequency domain). The objective is to develop a computationally efficient dictionary learning approach that emphasizes large-scale spatial connectivity patterns. This is achieved by removing the strong spatial correlations in the training data, thereby eliminating a large number of insignificant components from the sparse learning computation. In addition to improving the computational complexity, sparse learning from low-rank training data sets suppresses the small-scale details from entering the reconstruction of large-scale connectivity patterns, thereby providing a regularization effect in solving the resulting ill-posed inverse problems. We apply the proposed approach to travel-time tomography inversion and nonlinear subsurface flow model calibration inverse problems to demonstrate its effectiveness and practicality.

Sparse representation is efficient to approximately recover signals by a linear composition of a few bases from an over-complete dictionary. However, in the scenario of data compression, its efficiency and popularity are hindered due to the extra overhead for encoding the sparse coefficients. Therefore, how to establish an accurate rate model in sparse coding and dictionary learning becomes meaningful, which has been not fully exploited in the context of sparse representation. According to the Shannon entropy inequality, the variance of data source can bound its entropy, thus can reflect the actual coding bits. Therefore, a Globally Variance-Constrained Sparse Representation (GVCSR) model is proposed, where a variance-constrained rate term is introduced to the conventional sparse representation. To solve the non-convex optimization problem, we employ the Alternating Direction Method of Multipliers (ADMM) for sparse coding and dictionary learning, both of which have shown state-of-the-art rate-distortion performance in image representation.

Feature learning that extracts concise and general- izable representations for data is one of the central problems in machine learning and signal processing. Sparse dictionary learning, also known as sparse coding, distinguishes from other feature learning techniques in sparsity exploitation, allowing the formulation of nonconvex optimizations that simultaneously uncover a structured dictionary and sparse representations. Despite the popularity of dictionary learning in applications, the landscapes of these optimizations that enable effective learning largely remain a mystery. This work characterizes the local optimization geometry for a simplified version of sparse coding where the L1 norm of the sparse coefficient matrix is minimized subject to orthogonal dictionary constraints. In particular, we show that the ground-truth dictionary and coefficient matrix are locally identifiable under the assumption that the coefficient matrix is sufficiently sparse and the number of training data columns is sufficiently large.

Blind separation of sparse sources from nonlinear mixtures

For face recognition, conventional dictionary learning (DL) methods have disadvantages. In the paper, we propose a novel robust, discriminative and comprehensive DL (RDCDL) model. The proposed model uses sample diversities of the same face image to make the dictionary robust. The model includes class-specific dictionary atoms and disturbance dictionary atoms, which can well represent the data from different classes. Both the dictionary and the representation coefficients of data on the dictionary introduce discriminative information, which improves effectively the discrimination capability of the dictionary. The proposed RDCDL is extensively evaluated on benchmark face image databases, and it shows superior performance to many state-of-the-art sparse representation and dictionary learning methods for face recognition.

Synthetic aperture radar (SAR) images are corrupted by speckle noise due to random interference of electromagnetic waves. In this paper, we proposed a speckle reduction technique based on sparse representation and dictionary learning. Firstly, an adaptive dictionary was learned by performing KSVD algorithm through a large amount of training patches extracted from the noisy SAR image. Considering the inaccurate recovery of point targets which is brought by the inadequate number of training samples, we employed a point target enhancing scheme to highlight the important point targets in the SAR image. Some experiments were conducted on real SAR images, and the results shows that our proposed algorithm can effectively reduce the speckle noise as well as preserve details. Some comparisons are made to prove its superiority to the available algorithms.

Facial Expression (FE) detection is a popular research area, particularly in the field of Image Classification, Pattern Recognition and Computer Vision. Sparse Representation (SR) and Dictionary Learning (DL) have significantly enhanced the classification performance of image recognition and also resolved the problem of the nonlinear distribution of face images and its implementation with DL. However, the locality structure of face image data containing more discriminative information, which is very critical for classification has not been fully explored by state-of-the-art existing SR-based approaches. Furthermore, similar coding results between test samples and neighboring training data, contained in the feature space are not being fully realized from the image features with similar image categorizations, to effectively capture the embedded discriminative information. In an attempt to resolve the forgoing issues, we propose a novel DL method, Convolutional locality-sensitive Dictionary Learning (CLSDL) for Facial Expression detection.

Compressed sensing based on dictionary learning for extracting impulse components

Abstract. Sparse representation and decoding is often used for denoising images and compression of images with respect to inherent features. In this paper, we adopt a methodology incorporating sparse representation of a snow cover change map using the K-SVD trained dictionary and sparse decoding to enhance the change map. The pixels often falsely characterized as "changes" are eliminated using this approach. The preliminary change map was generated using differenced NDSI or S3 maps in case of Resourcesat-2 and Landsat 8 OLI imagery respectively. These maps are extracted into patches for compressed sensing using Discrete Cosine Transform (DCT) to generate an initial dictionary which is trained by the K-SVD approach. The trained dictionary is used for sparse coding of the change map using the Orthogonal Matching Pursuit (OMP) algorithm. The reconstructed change map incorporates a greater degree of smoothing and represents the features (snow cover changes) with better accuracy. The enhanced change map is segmented using kmeans to discriminate between the changed and non-changed pixels. The segmented enhanced change map is compared, firstly with the difference of Support Vector Machine (SVM) classified NDSI maps and secondly with a reference data generated as a mask by visual interpretation of the two input images. The methodology is evaluated using multi-spectral datasets from Resourcesat-2 and Landsat-8. The k-hat statistic is computed to determine the accuracy of the proposed approach.