Non-negative and local sparse coding based on l2-norm and Hessian regularization

Image representation based on sparse coding generalizes the bag of words model. Although it reduces the reconstruction error for local features to achieve the state-of-the-art image classification performance, the large computational cost hinders the application of sparse coding-based image features. In this paper, we propose approximating a sparse code using the output of a simple neural network. The resulting parameter learning model for the neural network automatically incorporates non-negative and shift-invariant constraints, leading to an efficient normalized non-negative sparse coding (N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> SC) sparse encoder. Without the use of the traditional iterative process to solve the sparse coding objective, the sparse encoder directly “converts” each local feature into a sparse code. We also introduce a method for training the encoder based on the auto-encoder method. In addition, we formally propose the corresponding sparse coding scheme called N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> SC, which enforces both the non-negative constraint and the shift-invariant constraint in addition to the traditional sparse coding criteria. As demonstrated by several experiments, the obtained N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> SC encoder requires only 3%-10% of the processing time for image feature extraction compared with the standard sparse coding scheme. At the same time, the features extracted using the exact solutions of the N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> SC coding scheme and the N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> SC encoder offer superior image classification accuracy compared to the accuracy of many existing sparse coding-based representations.

Graph construction using adaptive Local Hybrid Coding scheme

Sparse coding-based transfer learning for energy disaggregation

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.

Impulsive wavelet based probability sparse coding model for bearing fault diagnosis

Image representation using local features and sparse coding (SC) plays a very important role in image classification when the dataset is fairly large. Despite of its worldwide popularity, there are still some improving space in classification efficiency and computational investment in training and coding phrase of SC. In this paper, we put forward a novel object categories recognition method from two aspects. First, the contextual relevance between image patches are fully utilized by merging local feature of every sub-patch with its neighboring ones into strong context features to generate the multiple sparse representations, which are received by the SC and multi-scale max pooling SPM(Spatial Pyramid Matching), respectively. Second, while calculating the sparse coefficients of SC, we need to solve L1-regularized least square problem. Screening out the zero coefficients and discarding the corresponding inactive codewords before solving Lasso problem can remarkably speed up the optimization. The proposed method outperforms state-of-the-art performance in a large number of image categorization experiments on several benchmarks: the ground truth dataset (21 Land-Use database), the event dataset (UIUC-Sport dataset), and the object recognition dataset (Caltech101 dataset).

Image representation using local features and sparse coding (SC) plays a very important role in image classification when the dataset is fairly large. Despite of its worldwide popularity, there are still some improving space in classification efficiency and computational investment in training and coding phrase of SC. In this paper, we put forward a novel object categories recognition method from two aspects. First, the contextual relevance between image patches are fully utilized by merging local feature of every sub-patch with its neighboring ones into strong context features to generate the multiple sparse representations, which are received by the SC and multi-scale max pooling SPM(Spatial Pyramid Matching), respectively. Second, while calculating the sparse coefficients of SC, we need to solve L1-regularized least square problem. Screening out the zero coefficients and discarding the corresponding inactive codewords before solving Lasso problem can remarkably speed up the optimization. The proposed method outperforms state-of-the-art performancein a large number of image categorization experiments on several benchmarks: the ground truth dataset (21 Land-Use database), the event dataset (UIUC-Sport dataset), and the object recognition dataset (Caltech101 dataset).

Sparse coding with morphology segmentation and multi-label fusion for hyperspectral image super-resolution

In computer vision, the bag-of-words (BoW) model has been widely applied to image related tasks, such as large scale image retrieval, image classification, and object categorization. The sparse coding (SC) method which leverages SC as a means of feature coding can guarantee both sparsity of coding vector and lower reconstruction error in the BoW model. Thus it can achieve better performance than the traditional vector quantization method. However, it suffers from the side effect introduced by the non-smooth sparsity regularizer that quite different words may be selected for similar patches to favor sparsity, resulting in the loss of correlation between the corresponding coding vectors. To address this problem, in this paper, we propose a novel soft assignment method based on index combination of top-2 large sparse codes of local descriptors to make the SC-based BoW tolerate the case of different word selection for similar patches. To further ensure similar patches select same words to generate similar coding vectors, we propose a collaborative dictionary learning method through imposing the sparse code similarity regularization factor along with the row sparsity regularization across data instances on top of group sparse coding. Experiments on the well-known public Oxford dataset demonstrate the effectiveness of our proposed methods.

Sparse coding allows the representation of complex data as a linear combination of basis sparse vectors (alternatively called atoms or codewords), a collection of which constitutes a dictionary. Dictionary learning is a learning process aimed at finding a small number of optimal basis vectors for a more accurate representation of the original data. The existing dictionary learning methods do not address the inherent uncertainty of the input data in their learning processes. To compensate for the uncertainty, and to obtain a flexible and effective learning system, we introduce a new adaptive fuzzy dictionary learning (AFDL) method for image classification purposes. The new method iteratively alternates between sparse coding based on a given dictionary and an adaptive fuzzy dictionary learning approach to learn (improve) dictionary atoms. The adjustability of the dictionary and coefficients vectors, in this method, provide us a more accurate and straight representation of input data. AFDL was applied on magnetic resonance images from the cancer image archive datasets, for medical image classification of cancer tumors. Finally, the overall experimental results clearly show that our approach outperforms its rival techniques in terms of accuracy, sensitivity, and specificity. Convergence speed in the experimental results shows that AFDL can achieve its acceptable precision in a reasonable time.

Recent research has shown the initial success of sparse coding (Sc) in solving many computer vision tasks. Motivated by the fact that kernel trick can capture the nonlinear similarity of features, which helps in finding a sparse representation of nonlinear features, we propose kernel sparse representation (KSR). Essentially, KSR is a sparse coding technique in a high dimensional feature space mapped by an implicit mapping function. We apply KSR to feature coding in image classification, face recognition, and kernel matrix approximation. More specifically, by incorporating KSR into spatial pyramid matching (SPM), we develop KSRSPM, which achieves a good performance for image classification. Moreover, KSR-based feature coding can be shown as a generalization of efficient match kernel and an extension of Sc-based SPM. We further show that our proposed KSR using a histogram intersection kernel (HIK) can be considered a soft assignment extension of HIK-based feature quantization in the feature coding process. Besides feature coding, comparing with sparse coding, KSR can learn more discriminative sparse codes and achieve higher accuracy for face recognition. Moreover, KSR can also be applied to kernel matrix approximation in large scale learning tasks, and it demonstrates its robustness to kernel matrix approximation, especially when a small fraction of the data is used. Extensive experimental results demonstrate promising results of KSR in image classification, face recognition, and kernel matrix approximation. All these applications prove the effectiveness of KSR in computer vision and machine learning tasks.

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.

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.

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.

A Novel Two-Dimensional Tensor Sparse Coding Algorithm for Image Representation