Globally Variance-Constrained Sparse Representation for Rate-Distortion Optimized Image Representation

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.

[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.

This paper proposes an adaptive image representation learning method for cervix cancer tumor detection. The method learns the representation in two stages, a local feature description using a sparse dictionary learning and a global image representation using a bag-of-features (BOF) approach. The resultant representation is thus a BOF histogram, learned from a sparse local patch representation. The parameters of the sparse learning representation algorithm are tuned up by searching dictionaries with low coherence and high sparsity. The proposed method was evaluated in a dataset of 394 cervical histology images with tumoral and non-tumoral pathologies acquired at a 10X magnification and a resolution of 3800 × 3000 pixels in RGB color. A conventional BOF image representation, using a linearized raw-block patch descriptor, was selected as the baseline. The preliminary results show that our proposed method improves the baseline for all different BOF dictionary sizes (125, 250, 500, 1000 and 2000). Under a 10 cross-validation test and a 2000 BOF dictionary, the best performance was 0:77±0:04 in average accuracy, improving in 2:5% the baseline. These results suggest that a learning-from-data approach could be used in different stages of an image classifier construction pipeline, in particular for the image representation stage.

Sparse representation and dictionary learning have been successfully applied to encode dense data and facilitate image classification. Though existing dictionary learning methods achieve better performance than their counterparts, the class discriminative ability of learned dictionary is still limited. This paper proposes a novel supervised dictionary learning method based on the prior of the block diagonal phenomenon, i.e., each sample should be well reconstructed by the samples in the same class while poorly reconstructed by the samples in other class. Specifically, a block diagonal regularizer is imposed on the affinity matrix to enforce the sparse representation matrix to have an approximately block diagonal structure, which makes the learned dictionary more discriminative and suitable for classification tasks. Furthermore, we present an effective optimization strategy by combining the alternating minimization with the alternating direction method of multipliers (ADMM) for the proposed framework. Experimental results on six real-world datasets show that the proposed method is more effective than state-of-the-art dictionary learning methods.

We propose a framework for automated detection of dry age-related macular degeneration (AMD) and diabetic macular edema (DME) from retina optical coherence tomography (OCT) images, based on sparse coding and dictionary learning. The study aims to improve the classification performance of state-of-the-art methods. First, our method presents a general approach to automatically align and crop retina regions; then it obtains global representations of images by using sparse coding and a spatial pyramid; finally, a multiclass linear support vector machine classifier is employed for classification. We apply two datasets for validating our algorithm: Duke spectral domain OCT (SD-OCT) dataset, consisting of volumetric scans acquired from 45 subjects—15 normal subjects, 15 AMD patients, and 15 DME patients; and clinical SD-OCT dataset, consisting of 678 OCT retina scans acquired from clinics in Beijing—168, 297, and 213 OCT images for AMD, DME, and normal retinas, respectively. For the former dataset, our classifier correctly identifies 100%, 100%, and 93.33% of the volumes with DME, AMD, and normal subjects, respectively, and thus performs much better than the conventional method; for the latter dataset, our classifier leads to a correct classification rate of 99.67%, 99.67%, and 100.00% for DME, AMD, and normal images, respectively.

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.

Dictionary learning aims to find a dictionary that can sparsely represent the training data. Methods in the literature typically solve the problem by alternating between two stages: sparse coding and dictionary update. In this paper, we propose a novel dictionary learning algorithm using rank-one projection (ROP). The key contribution is that we cast dictionary learning as an optimization with respect to a single variable which is a set of rank one matrices. The resulting algorithm is hence single-stage. An alternating direction method of multipliers (ADMM) is derived to solve the optimization problem and a lower bound of penalty parameter is computed to guarantee a global convergence despite non-convexity of the optimization formulation. From practical point of view, ROP reduces the number of tuning parameters required in benchmark algorithms. Numerical tests demonstrate that ROP outperforms benchmark algorithms for both synthetic and real data.

The coronavirus disease 2019 (COVID-19) is a fast transmitting virus spreading throughout the world and causing a pandemic. Early detection of the disease is crucial in preventing the rapid propagation of the virus. Although Computed Tomography (CT) technology is not considered to be a reliable first-line diagnostic tool, it does have the potential to detect the disease. While several high performing deep learning networks have been proposed for the automated detection of the virus using CT images, deep networks lack the explainability, clearness, and simplicity of other machine learning methods. Sparse representation is an effective tool in image processing tasks with an efficient algorithm for implementation. In addition, the output sparse domain can be easily mapped to the original input signal domain, thus the features provide information about the signal in the original domain. This work utilizes two sparse coding algorithms, frozen dictionary learning, and label-consistent k-means singular value decomposition (LC-KSVD), to help classify Covid-19 CT lung images. A framework for image sparse coding, dictionary learning, and classifier learning is proposed and an accuracy of $$89\%$$ is achieved on the cleaned CC-CCII CT lung image dataset.

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.

Effective representation methods and proper signal priors are crucial in most signal processing applications. In this thesis we focus on different structured models and we design appropriate schemes that allow the discovery of low dimensional latent structures that characterise and identify the signals. Motivated by the highly non-linear structure of most datasets, we firstly investigate the geometry of manifolds. Manifolds are low dimensional, non-linear structures that are naturally employed to describe sets of strongly related signals such as the images of a 3-D object captured from different viewpoints. However, the use of manifolds in applications is not straightforward due to their usually non-analytic and non-linear form. We propose here a way to `disassemble' a manifold into simpler components by approximating it with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that can represent manifold data accurately while preserving the manifold's structure. To this end, we employ a greedy technique that iteratively merges manifold samples into groups based on the difference of local tangents. We use our algorithm to approximate synthetic and real manifolds and to demonstrate that it is competitive to state-of-the-art techniques. Then, we consider structured sparse representations of signals and we propose a new sparsity model, where signals are essentially composed of a small number of structured {\it molecules }. We define the molecules to be linear combinations of a small number of atoms in a redundant dictionary. Our multi-level model takes into account the energy distribution of the significant signal components in addition to their support. It permits to define typical visual patterns and recognise them in prototypical or deformed form. We define a new structural difference measure between molecules and their deformed versions, which is based on their sparse codes and we create an algorithm for decomposing signals into molecules that can account for different deviations in the internal molecule structure. Our experiments verify the benefits of the new image model in various restoration tasks and they confirm that the development of proper models that extend the mere notion of sparsity can be very useful for various inverse problems in imaging. Finally, we investigate the problem of learning molecule representations directly in the sparse code domain. We constrain sparse codes to be linear combinations of a few, possibly deformed, molecules and we design an algorithm that can learn the structure from the codes without transforming them back into the signal domain. To this end, we take advantage of our structural difference which is based on the sparse codes and we devise a scheme for representing the codes with molecules and learn the molecules at the same time. To illustrate the effectiveness of our proposed algorithm we apply it to various synthetic and real datasets and we compare the results with traditional sparse coding and dictionary learning techniques. From the experiments, we verify the superior performance of our scheme in interpreting and recognising correctly the underlying structure. In short, in this thesis we are interested in low-dimensional, structured models. Among the various choices, we focus on manifolds and sparse representations and we propose schemes that enhance their structural properties and highlight their effectiveness in signal representations.

In recent years, sparse coding via dictionary learning has been widely used in many applications for exploiting sparsity patterns of data. For classification, useful sparsity patterns should have discrimination, which cannot be well achieved by standard sparse coding techniques. In this paper, we investigate structured sparse coding for obtaining discriminative class-specific group sparsity patterns in the context of classification. A structured dictionary learning approach for sparse coding is proposed by considering the \(\ell _{2,0}\) norm on each class of data. An efficient numerical algorithm with global convergence is developed for solving the related challenging \(\ell _{2,0}\) minimization problem. The learned dictionary is decomposed into class-specific dictionaries for the classification that is done according to the minimum reconstruction error among all the classes. For evaluation, the proposed method was applied to classifying both the synthetic data and real-world data. The experiments show the competitive performance of the proposed method in comparison with several existing discriminative sparse coding methods.

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.

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.

In this paper, we focus on sparse dictionary learning that is widely used as a data processing technique in many real-world applications. Based on the frame of alternating direction method of multiplier (ADMM), we extend to an alternating direction and projection method for sparse dictionary learning. By introducing proximal mapping and the equivalence to the corresponding projection, a partial convergence result of this multi-block and nonconvex ADMM algorithm is given that the algorithm converges to a Karush-Kuhn-Tucker point whenever it converges.