Sparse image representations with shift-invariant tree-structured dictionaries

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.

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.

An encryption algorithm based on sparse coding and compressive sensing is proposed. Sparse coding is used to find the sparse representation of images as a linear combination of atoms from an overcomplete learned dictionary. The overcomplete dictionary is learned using K-SVD, utilizing non-overlapping patches obtained from a set of images. Compressed sensing is used to sample data at a rate below the Nyquist rate. A Gaussian measurement matrix compressively samples the plain image. As these measurements are linear, chaos based permutation and substitution operations are performed to obtain the cipher image. Bit-level scrambling and block substitution is done to confuse and diffuse the measurements. Simulation results verify the performance of the proposed technique against various statistical attacks.

In order to solve the issue of ignoring the successive and dynamic lip motion information in traditional audio-visual speech synchrony analysis models, a novel method based on shift-invariant learned dictionary is presented. In this method, sparse representation with shift-invariant dictionary is introduced to analyze the bimodal structure of articulation. The learned dictionary is obtained based on the audio-visual coherence dictionary learning algorithm, and the dynamic correlation between voice and lip motion of diverse syllable or word is represented as a pattern by this audio-visual coherence atom. According to these utterance patterns, an original audio-visual synchronization score measuring scheme is proposed. The results of the experiment on four different asynchronous data show the good performance of the method.

In recent years, sparse coding has drawn considerable research attention in developing feature representations for visual recognition problems. In this paper, we devise sparse coding algorithms to learn a dictionary of basis functions from Scale- Invariant Feature Transform (SIFT) descriptors extracted from images. The learned dictionary is used to code SIFT-based inputs for the feature representation that is further pooled via spatial pyramid matching kernels and fed into a Support Vector Machine (SVM) for object classification on the large-scale ImageNet dataset. We investigate the advantage of SIFT-based sparse coding approach by combining different dictionary learning and sparse representation algorithms. Our results also include favorable performance on different subsets of the ImageNet database.

K-Singular Value Decomposition (K-SVD) is an excellent feature analysis method, but it has a large amount of calculation and low algorithm efficiency. To solve the above problems, a dictionary learning method for image block classification training is proposed. This method uses image entropy as the classification index of image samples, selects more complex texture image blocks with more analytical value, and uses Discrete Cosine Transform- Discrete Wavelet Transformation (DCT-DWT) dictionary to train them in K-Singular Value Decomposition. Through the feedback of sparse coefficients, the threshold value is dynamically changed and the precision of sparse coding is controlled. In the sparse solution, a variable-step Orthogonal Matching Pursuit (OMP) algorithm is used. The experimental comparison shows that the classification K-Singular Value Decomposition dictionary learning algorithm runs faster, and the Peak signal-to-noise Ratio (PSNR) and Structural Similarity (SSIM) value of the reconstructed image are higher.

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.

In many applications signals reside on the vertices of weighted graphs. Thus, there is the need to learn low dimensional representations for graph signals that will allow for data analysis and interpretation. Existing unsupervised dimensionality reduction methods for graph signals have focused on dictionary learning. In these works the graph is taken into consideration by imposing a structure or a parametrization on the dictionary and the signals are represented as linear combinations of the atoms in the dictionary. However, the assumption that graph signals can be represented using linear combinations of atoms is not always appropriate. In this paper we propose a novel representation framework based on non-linear and geometry-aware combinations of graph signals by leveraging the mathematical theory of Optimal Transport. We represent graph signals as Wasserstein barycenters and demonstrate through our experiments the potential of our proposed framework for low-dimensional graph signal representation.

Sparse representation based classification has led to interesting image recognition results, while the dictionary used for sparse coding plays a key role in it. This paper presents a novel dictionary learning (DL) method to improve the pattern classification performance. Based on the Fisher discrimination criterion, a structured dictionary, whose dictionary atoms have correspondence to the class labels, is learned so that the reconstruction error after sparse coding can be used for pattern classification. Meanwhile, the Fisher discrimination criterion is imposed on the coding coefficients so that they have small within-class scatter but big between-class scatter. A new classification scheme associated with the proposed Fisher discrimination DL (FDDL) method is then presented by using both the discriminative information in the reconstruction error and sparse coding coefficients. The proposed FDDL is extensively evaluated on benchmark image databases in comparison with existing sparse representation and DL based classification methods.

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.

The use of a person's signature is considered as one of the most commonly used biometric methods for recognition, either as a standalone feature or as part of multimodal systems. Based on the inter-writer variability, handwritten signatures have been accepted as a personal trait in many transactions to verify the consent or the author's presence. The main challenges for handwritten signature verification are the limited amount of available data for each writer and the intra-writer variability. Sparse Representation (i.e. dictionary learning and sparse coding) achieved state of the art results at handwritten signature verification, using only a small set of genuine reference samples of the writer. The extension of Sparse Representation to an efficient multi-layer architecture is Deep Sparse Coding. Deep Sparse Coding architecture connects multiple layers of Sparse Representation with a sparse-to-dense module in order to enable Sparse Coding on deeper layers. Learning sparse representations at different levels of abstraction leads to building feature hierarchies. The sparse-to-dense module involves a Dimensionality Reduction process, which was implemented with simple and fast methods, such as Random Orthogonal projection or PCA; instead of the computational expensive DrLIM. The performance of the proposed Deep Sparse Coding architecture to the challenging problem of offline signature verification is demonstrated in the popular CEDAR signature dataset, delivering improved state of the art results.

Computing sparse representation (SR) over an exemplar dictionary is time consuming and computationally expensive for large dictionary size. This also requires huge memory requirement for saving the dictionary. In order to reduce the latency and to achieve some diversity, ensemble of exemplar dictionary based language identification (LID) system is explored. The full diversity can be obtained if each of the exemplar dictionary contains only one feature vector from each of the language class. To achieve full diversity, a large number of multiple dictionaries are required; thus needs to compute SR for a particular test utterance as many times. The other solution to reduce the latency is to use a learned dictionary. The dictionary may contain unequal number of dictionary atoms and it is not guaranteed that each language class information is present. It totally depends upon the number of data and its variations. Motivated by this, language specific dictionary is learned, and then concatenated to form a single learned dictionary. Furthermore, to overcome the problem of ensemble exemplar dictionary based LID system, we investigated the ensemble of learned-exemplar dictionary based LID system. The proposed approach achieves the same diversity and latency as that of ensemble exemplar dictionary with reduced number of learned dictionaries. The proposed techniques are applied on two spoken utterance representations: the i-vector and the JFA latent vector. The experiments are performed on 2007 NIST LRE, 2009 NIST LRE and AP17-OLR datasets in closed set condition.

Tensor-based sparse representations of multi-phase medical images for classification of focal liver lesions

Image fusion aims to merge two or more images captured via various sensors of the same scene to construct a more informative image by integrating their details. Generally, such integration is achieved through the manipulation of the representations of the images concerned. Sparse representation plays an important role in the effective description of images, offering a great potential in a variety of image processing tasks, including image fusion. Supported by sparse representation, in this paper, an approach for image fusion by the use of a novel dictionary learning scheme is proposed. The nonlocal self-similarity property of the images is exploited, not only at the stage of learning the underlying description dictionary but during the process of image fusion. In particular, the property of nonlocal self-similarity is combined with the traditional sparse dictionary. This results in an improved learned dictionary, hereafter referred to as the nonlocal sparse K-SVD dictionary (where K-SVD stands for the K times singular value decomposition that is commonly used in the literature), and abbreviated to NL_SK_SVD. The performance of the NL_SK_SVD dictionary is applied for image fusion using simultaneous orthogonal matching pursuit. The proposed approach is evaluated with different types of images, and compared with a number of alternative image fusion techniques. The resultant superior fused images using the present approach demonstrates the efficacy of the NL_SK_SVD dictionary in sparse image representation.

An important way for people to obtain information is vision. However, during the collection and transmission of digital images, there is often some noise that is not good for people to get information quickly and correctly. Therefore, before the image processing analysis, the image denoising pretreatment is particularly important. However, the traditional denoising method will lose the details of the image and the result of denoising is unsatisfactory. In recent years, with the continuous improvement of sparse representation theory, it has also made great progress in image processing and has been well applied in image denoising, which has become one of the most effective methods in current image denoising methods. Using sparse coding decomposes the image on sparse domain, and the handling of the sparse coefficient by setting threshold. And based on a sparse representation of an overly-complete dictionary, an image is represented by a linear combination of atoms in the dictionary. Its adaptability also brings better denoising effect.