Semi-supervised Learning by Sparse Representation

In this paper we propose a novel face hallucination algorithm to synthesize a high-resolution face image from several low-resolution input face images. As described in Liu et al. [8]'s work, face hallucination uses two models: a global parametric model which synthesizes global face shapes from eigenfaces, and a local parametric model which enhances the local high frequency details. We follow a similar process to develop a robust face hallucination algorithm. Firstly, we obtain eigenfaces from a number of low resolution face images extracted from a video sequence using a face tracking algorithm. Then we compute the difference between the interpolated low-resolution face and the mean face, and use this difference face as the query to retrieve approximate sparse eigenfaces representation. The eigenfaces are combined using the coefficients obtained from sparse representation and added into the interpolated low-resolution face. In this way, the global shape of the interpolated low resolution face can be successfully enhanced. Secondly, we improve the example-based super-resolution method [7] for local high frequency information enhancement. Our proposed algorithm uses the Approximate Nearest Neighbors (ANN) search method to find a number of nearest neighbors for a stack of queries, instead of finding the exact match for each low frequency patch as presented in [7]. Median filtering is used to remove the noise from the nearest neighbors in order to enhance the signal. Our proposed algorithm uses sparse representation and the ANN method to enhance both global face shape and local high frequency information while greatly improving the processing speed, as confirmed empirically.

Machine Learning is a modern and actively developing field of computer science, devoted to extracting and estimating dependencies from empirical data. It combines such fields as statistics, optimization theory and artificial intelligence. In practical tasks, the general aim of Machine Learning is to construct algorithms able to generalize and predict in previously unseen situations based on some set of examples. Given some finite information, Machine Learning provides ways to exract knowledge, describe, explain and predict from data. Kernel Methods are one of the most successful branches of Machine Learning. They allow applying linear algorithms with well-founded properties such as generalization ability, to non-linear real-life problems. Support Vector Machine is a well-known example of a kernel method, which has found a wide range of applications in data analysis nowadays. In many practical applications, some additional prior knowledge is often available. This can be the knowledge about the data domain, invariant transformations, inner geometrical structures in data, some properties of the underlying process, etc. If used smartly, this information can provide significant improvement to any data processing algorithm. Thus, it is important to develop methods for incorporating prior knowledge into data-dependent models. The main objective of this thesis is to investigate approaches towards learning with kernel methods using prior knowledge. Invariant learning with kernel methods is considered in more details. In the first part of the thesis, kernels are developed which incorporate prior knowledge on invariant transformations. They apply when the desired transformation produce an object around every example, assuming that all points in the given object share the same class. Different types of objects, including hard geometrical objects and distributions are considered. These kernels were then applied for images classification with Support Vector Machines. Next, algorithms which specifically include prior knowledge are considered. An algorithm which linearly classifies distributions by their domain was developed. It is constructed such that it allows to apply kernels to solve non-linear tasks. Thus, it combines the discriminative power of support vector machines and the well-developed framework of generative models. It can be applied to a number of real-life tasks which include data represented as distributions. In the last part of the thesis, the use of unlabelled data as a source of prior knowledge is considered. The technique of modelling the unlabelled data with a graph is taken as a baseline from semi-supervised manifold learning. For classification problems, we use this apporach for building graph models of invariant manifolds. For regression problems, we use unlabelled data to take into account the inner geometry of the input space. To conclude, in this thesis we developed a number of approaches for incorporating some prior knowledge into kernel methods. We proposed invariant kernels for existing algorithms, developed new algorithms and adapted a technique taken from semi-supervised learning for invariant learning. In all these cases, links with related state-of-the-art approaches were investigated. Several illustrative experiments were carried out on real data on optical character recognition, face image classification, brain-computer interfaces, and a number of benchmark and synthetic datasets.

Significant advances in compressive sensing and sparse signal encoding have provided a rich set of mathematical tools for signal analysis and representation. In addition to novel formulations for enabling sparse solutions to underdetermined systems, exciting progress has taken place in efficiently solving these problems from an optimization theoretic viewpoint. The focus of the wide body of literature in compressive sensing/sparse signal representations has however been on the problem of signal recovery from a small number of measurements (equivalently a sparse coefficient vector). This tutorial will discuss the design of sparse signal representations explicitly for the purposes of signal classification. The tutorial will focus on and build upon two significant recent advances. First, the work by Wright et al. which advocates the use of a dictionary (or basis) matrix comprising of class-specific training sub-dictionaries. In this framework, a test signal is modeled as a sparse linear combination of training vectors in the dictionary, sparsity being enforced by the assertion that only coefficients corresponding to one class (from which the test signal is drawn) ought to be active. The second set of ideas we leverage are recent key contributions in model-based compressive sensing where prior information or constraints on sparse coefficients are used to enhance signal recovery. These ideas will be combined towards the exposition of current trends: namely the development of class-specific priors or constraints to capture structure on sparse coefficients that helps explicitly distinguish between signal classes. In the second part of the tutorial, applications will be discussed including: 1.) structured sparsity for classification of medical imagery for diagnostics, 2.) low-rank approximation and sparse recovery for visual data reconstruction, and 3.) sparse representations for target detection and classification in hyperspectral imagery (guest speaker from the US Army Research Lab).

Dictionary learning plays an important role in machine learning, where data vectors are modeled as a sparse linear combinations of basis factors (i.e., dictionary). However, how to conduct dictionary learning in noisy environment has not been well studied. Moreover, in practice, the dictionary (i.e., the lower rank approximation of the data matrix) and the sparse representations are required to be nonnegative, such as applications for image annotation, document summarization, microarray analysis. In this paper, we propose a new formulation for non-negative dictionary learning in noisy environment, where structure sparsity is enforced on sparse representation. The proposed new formulation is also robust for data with noises and outliers, due to a robust loss function used. We derive an efficient multiplicative updating algorithm to solve the optimization problem, where dictionary and sparse representation are updated iteratively. We prove the convergence and correctness of proposed algorithm rigorously.We show the differences of dictionary at different level of sparsity constraint.The proposed algorithm can be adapted for clustering and semi-supervised learning.

According to the image processing theory, complex texture image regions have larger entropy values, an adaptive steganography algorithm in the sparse domain is proposed here. The algorithm first divides an image into nonoverlapping image blocks, then computes the entropy of each block and chooses the mean of all entropies as a threshold. Image blocks whose entropy is higher than the threshold are selected for sparse decomposition as complex texture image regions. The secret message is embedded into the decomposition coefficients, and then the stego image is reconstructed with modified coefficients. The experimental results prove that, given the same payload, the proposed adaptive algorithm has a better performance against the steganalyzer.

Sparse representation provides an efficient way for the compression of hyperspectral images in the literature. In this work, an improved version of the Spectral-Spatial Adaptive Sparse Representation (SSASR), Modified SSASR (MSSASR), is proposed for hyperspectral image compression. In the first step of the proposed method, superpixel maps are generated for adaptive spatio-spectral representation. Then, the best possible dictionary is computed for the representation of the data. Afterwards, sparse coefficients are determined depending on the dictionary by Simultaneous Orthogonal Matching Pursuit (SOMP) method. In the final step, the dictionary and sparse coefficients are encoded by quantization and entropy encoding. This paper has the following novelties: modified dictionary learning step, new ordering scheme and Differential Pulse Code Modulation (DPCM) usage. Owing to modified dictionary learning, the sparse coefficients can be represented more compact than traditional SSASR. By using of new ordering scheme, it is not needed to send the superpixel map as side information. Moreover, DCPM usage lowers the magnitudes of sparse coefficients. Thanks to these modifications, the proposed method achieves an important improvement on compression performance. In the experimental results, the proposed method is compared with PCA+JPEG2000, DWT+JPEG2000, 3D-SPECK, 3D-TARP and SSASR methods on Indian Pines, Washington DC Mall, Jasper Ridge and Moffett Field scenes. The evaluation is carried out not only using distance and similarity metrics, namely, signal-to-noise ratio, mean spectral angle and mean spectral correlation metrics but also computation times. Additionally, reconstruction quality in anomaly regions is also used for comparison. Experimental results show that the proposed method outperforms the other compression methods in terms of quality metrics and anomaly preserving performance.

The novel motion compensation method, called LIC (Local Intensity Compensation), approximates a current block using a linear combination of reference blocks. To reduce the bitrate of high quality images, sparse coefficients are preferable; then, a method applying sparse representation to the LIC has been proposed. A solver of sparse representation called AIHT (Accelerated Iterative Hard Thresholding) uses many vector and matrix operations, and video coding standards encode frames in GOP (Group Of Pictures) structure. In some cases, video coding methods have to encode videos in real time, but the LIC using sparse representation takes a large amount of computational time for the prediction; thus, this paper demonstrates a method to accelerate the LIC using sparse representation as follows: (i) acceleration of the AIHT itself using GPU (Graphics Processing Unit); and (ii) employing parallel processing in multi-core CPU, namely OpenMP, for the independent structure of the GOP. By using OpenMP, multiple GPUs work under different cores. Experimental results show that the methods (i) and (ii) are faster than CPU implementation by about 4 times and about 7.4 times maximum, respectively.

A semi-supervised deep learning approach for cropped image detection

Semi-supervised matrixized least squares support vector machine

A novel sparse representation based multi-source localization method is presented in this work. We envision a wireless network infrastructure containing multiple phase arrays of acoustic sensors. With multiple arrays, direct estimation of a set of source locations is achieved using a new joint sparse representation of array covariance matrices (JSRACM). This representation transforms the source location estimation problem into a spatial sparse signal representation (SSSR) optimization problem. To mitigate the high computation complexity of JSRACM, a novel binary sparse indicative vector (SIV) is introduced to represent the support of joint SSSR of array covariance matrices. As such, the multiple source locations may be estimated by solving an unconstrained optimization problem of the SIV vector using existing FOCUSS-like algorithms. The resulting SIVR-JSRACM algorithm does not require prior information of the number of sources nor initial source location estimates. It promises super-resolution, robustness to noise, and low computing complexity which is independent of the number of sensor phase arrays. Simulation results demonstrate superior performance of the proposed algorithm.

By means of a sparse collaborative representation mechanism, sparse-representation-based classifiers show a superior performance in hyperspectral image (HSI) classification. Exploiting the similarity and distinctiveness of HSI neighboring pixels, we propose a new nearest regularized joint sparse representation (NRJSR) classification method in this letter. In the classification process of the central test pixel, the weights of different neighboring pixels and the sparse representation coefficients of different training samples are optimized simultaneously within a regularized sparsity model, which can obtain adaptive weights with good joint sparse representation ability. An alternative iteration strategy is used to solve the regularized joint sparsity model. The proposed NRJSR algorithm is tested on two benchmark HSI data sets. Experimental results demonstrate that the proposed algorithm performs better than other sparsity-based algorithms and spectral and spectral–spatial support vector machine classifiers.

To improve the quality of the fused image, we propose a remote sensing image fusion method based on sparse representation. In the method, first, the source images are divided into patches and each patch is represented with sparse coefficients using an overcomplete dictionary. Second, the larger value of sparse coefficients of panchromatic (Pan) image is set to 0. Third, Then the coefficients of panchromatic (Pan) and multispectral (MS) image are combined with the linear weighted averaging fusion rule. Finally, the fused image is reconstructed from the combined sparse coefficients and the dictionary. The proposed method is compared with intensity-hue-saturation (IHS), Brovey transform (Brovey), discrete wavelet transform (DWT), principal component analysis (PCA) and fast discrete curvelet transform (FDCT) methods on several pairs of multifocus images. The experimental results demonstrate that the proposed approach performs better in both subjective and objective qualities.

To improve the quality of the fused image, we propose a remote sensing image fusion method based on sparse representation. In the method, first, the source images are divided into patches and each patch is represented with sparse coefficients using an overcomplete dictionary. Second, the larger value of sparse coefficients of panchromatic (Pan) image is set to 0. Third, Then the coefficients of panchromatic (Pan) and multispectral (MS) image are combined with the linear weighted averaging fusion rule. Finally, the fused image is reconstructed from the combined sparse coefficients and the dictionary. The proposed method is compared with intensity-hue-saturation (IHS), Brovey transform (Brovey), discrete wavelet transform (DWT), principal component analysis (PCA) and fast discrete curvelet transform (FDCT) methods on several pairs of multifocus images. The experimental results demonstrate that the proposed approach performs better in both subjective and objective qualities.

In this paper, a semi-supervised dimensionality reduction method based on sparse representation is proposed. The s-parse representation has the ability to distinguish samples, exactly, the sparse coefficient in sparse representation will be large when the represented samples and the entries of the dictionary are in the same class, but it will be small if they are not. So we use the sparse coefficient to construct our l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -graph in which the connection weight is defined as the contribution of each entries in the dictionary when construct this sample. Considering the goal that reduce the dimension of each pixel and preserve the discriminative information as much as possible we propose an regularization term incorporating the structures reflected by l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -graph. Although labeled samples are always insufficient in HSI processing, we make full use of them with abundant unlabeled samples to improve the performance after dimensionality reduction. So we then introduce LDA method and extend it as a semi-supervised method. Finally we evaluate our method in practical classification work and experimental results on real hyperspectral image show that the proposed method can achieve better and more stable results.

Recently, sparse representation based methods have proven to be successful towards solving image restoration problems. The objective of these methods is to use sparsity prior of the underlying signal in terms of some dictionary and achieve optimal performance in terms of mean-squared error, a metric that has been widely criticized in the literature due to its poor performance as a visual quality predictor. In this work, we make one of the first attempts to employ structural similarity (SSIM) index, a more accurate perceptual image measure, by incorporating it into the framework of sparse signal representation and approximation. Specifically, the proposed optimization problem solves for coefficients with minimum norm and maximum SSIM index value. Furthermore, a gradient descent algorithm is developed to achieve SSIM-optimal compromise in combining the input and sparse dictionary reconstructed images. We demonstrate the performance of the proposed method by using image denoising and super-resolution methods as examples. Our experimental results show that the proposed SSIM-based sparse representation algorithm achieves better SSIM performance and better visual quality than the corresponding least square-based method.