Quick Response (QR) codes usage in e-commerce is on the rise due to their versatility and ability to connect offline and online content, taking over almost every aspect of a business from posters to ...payments. Thus, many efforts have aimed at improving the visual quality of QR codes to be easily included in publicity designs in billboards and magazines. The most successful approaches, however, are slow since optimization algorithms are required for the generation of each beautified QR code, hindering its online customization. The aim of this paper is the fast generation of visually pleasant and robust QR codes. The proposed framework leverages state-of-the-art deep-learning algorithms to embed a color image into a baseline QR code in seconds while keeping a maximum probability of error during the decoding procedure. Halftoning techniques that exploit the human visual system (HVS) are used to smooth the embedding of the QR code structure in the final QR code image while reinforcing the decoding robustness. Compared to optimization-based methods, our framework provides similar qualitative results but is 3 orders of magnitude faster.
•The calculation of graph similarity matrix in spectral clustering is computational complex for the large high-dimensional data sets.•The similarity matrix can be obtained using matrix completion ...method to improve the computational efficiency.•The Schatten capped p norm used in this paper integrates the rank norm, nuclear norm, and the Schatten p norm.•The split Bregman algorithm based on the Schatten capped p norm and randomized singular value decomposition is developed to accelerate the convergence of matrix completion.
Spectral clustering (SC) is a widely used technique to perform group unsupervised classification of graph signals. However, SC is sometimes computationally intensive due to the need to calculate the graph similarity matrices on large high-dimensional data sets. This paper proposes an efficient SC method that rapidly calculates the similarity matrix using a matrix completion algorithm. First, a portion of the elements in the similarity matrix are selected by a blue noise sampling mask, and their similarity values are calculated directly from the original dataset. After that, a split Bregman algorithm based on the Schatten capped p norm is developed to rapidly retrieve the rest of the matrix elements. Finally, spectral clustering is performed based on the completed similarity matrix. A set of simulations based on different data sets are used to assess the performance of the proposed method. It is shown that for a sufficiently large sampling rate, the proposed method can accurately calculate the completed similarity matrix, and attain good clustering results while improving on computational efficiency.
We presented a method based on multigraphs to mathematically define a distribution function in time for the generation of data exchange in a special-purpose communication network. This is needed for ...the modeling and design of communication networks (CNs) consisting of integrated telecommunications and computer networks (ITCN). Simulation models require a precise definition of network traffic communication. An additional problem for describing the network traffic in simulation models is the mathematical model of data distribution, according to which the generation and exchange of certain types and quantities of data are realized. The application of multigraphs enabled the time and quantity of the data distribution to be displayed as operational procedures for a special-purpose communication unit. A multigraph was formed for each data-exchange time and allowed its associated adjacency matrix to be defined. Using the matrix estimation method allowed the mathematical definition of the distribution function values. The application of the described method for the use of multigraphs enabled a more accurate mathematical description of real traffic in communication networks.
Hypergraph neural networks (HyperGNNs) are a family of deep neural networks designed to perform inference on hypergraphs. HyperGNNs follow either a spectral or a spatial approach, in which a ...convolution or message-passing operation is conducted based on a hypergraph algebraic descriptor. While many HyperGNNs have been proposed and achieved state-of-the-art performance on broad applications, there have been limited attempts at exploring high-dimensional hypergraph descriptors (tensors) and joint node interactions carried by hyperedges. In this article, we depart from hypergraph matrix representations and present a new tensor-HyperGNN (T-HyperGNN) framework with cross-node interactions (CNIs). The T-HyperGNN framework consists of T-spectral convolution, T-spatial convolution, and T-message-passing HyperGNNs (T-MPHN). The T-spectral convolution HyperGNN is defined under the t-product algebra that closely connects to the spectral space. To improve computational efficiency for large hypergraphs, we localize the T-spectral convolution approach to formulate the T-spatial convolution and further devise a novel tensor-message-passing algorithm for practical implementation by studying a compressed adjacency tensor representation. Compared to the state-of-the-art approaches, our T-HyperGNNs preserve intrinsic high-order network structures without any hypergraph reduction and model the joint effects of nodes through a CNI layer. These advantages of our T-HyperGNNs are demonstrated in a wide range of real-world hypergraph datasets. The implementation code is available at https://github.com/wangfuli/T-HyperGNNs.git.
Currently, there is an increasing need to develop tools that allow the processing and exploitation of the massive amount of data available in many fields, such as computer vision, biology, social ...sciences, computational image, and others. The proposed research focuses on developing novel theories and algorithms that enable learning from data containing high-order inter-relationships. In particular, in data modeled by graphs and hypergraphs structures, the applications range from embedding images into QR codes to classification and denoising in a myriad of fields. Graph signal processing (GSP) techniques are powerful tools that model complex relationships within large datasets and are now used in a number of applications in different areas, including data science, communication networks, epidemiology, and sociology. Simple graphs, however, can only model pairwise relationships among data, preventing their application in modeling networks with higher-order relationships. In representation learning, for instance, considering high-order relationships in data has recently shown to be superior in many applications. For this reason, some efforts have been made to generalize well-known graph signal processing techniques to more complex graphs, such as hypergraphs, which allow for capturing higher-order relationships among data. In this dissertation, we provide a new hypergraph signal processing framework (t-HGSP) based on a novel tensor-tensor product algebra that has emerged as a powerful tool for preserving the intrinsic structures of tensors. The proposed framework allows the generalization of traditional GSP techniques while keeping the dimensionality characteristic of the complex systems represented by hypergraphs. To this end, the core elements of the t-HGSP framework are introduced, including the shifting operators and the hypergraph signal. The hypergraph Fourier space is also defined, followed by the concept of bandlimited signals and sampling. These tools are not only useful in the areas of hypergraph signal processing but also enable representation learning applications such as tensor-based hypergraph neural networks. Key to the success of hypergraph-based methods is having a meaningful hypergraph that may only be readily available for some applications. Nonetheless, having laid down the essential tools for t-HGSP opens the door for learning the hypergraph topology that dictates the higher-order relationships among the data. Hence, in this work, we also address the challenge of learning the underlying hypergraph topology from the data. As in graph signal processing applications, we consider the case in which the data possesses certain regularity or smoothness on the hypergraph. Given the hypergraph spectrum and frequency coefficient definitions provided by the t-HGSP framework, we propose a method to learn the hypergraph Laplacian from a set of smooth signals by minimizing their total variation on the hypergraph (TVL-HGSP). Additionally, we introduce an alternative approach (PDL-HGSP) that takes advantage of primal-dual-based algorithms and approximations to reduce time and space complexity. Finally, in representation learning, we depart from existing matrix representations of hypergraphs and combine the proposed learning algorithms with novel tensor-based hypergraph convolutional neural networks to propose hypergraph learning-convolutional neural networks (t-HyperGLNN). Compared to state-of-the-art, the learned adjacency tensor provides a more robust representation in high dimensions and the hypergraph signal model joint effects among connected nodes. Throughout this dissertation, we validate, theoretically and experimentally, that the proposed methods offer significant gains over the state-of-the-art in different applications, which include clustering, denoising, classification, and embedding of QR codes. For the latter, we proposed a fast generation of visually pleasant and robust QR codes. The proposed framework leverages the proposed hypergraph-based algorithms and state-of-the-art deep-learning algorithms to embed a color image into a baseline QR code in seconds while keeping a maximum error probability during the decoding procedure.
Light detection and ranging (LiDAR) remote sensing systems are deployed in various platforms including satellites, airplanes, and drones—which, in essence, determines the sampling characteristics of ...the underlying imaging system. Low-altitude LiDARs provide high photon count and high spatial resolution but only in very localized patches. Satellite LiDARs, on the other hand, provide measurements at a global scale but are limited by low photon count and their samples are sparsely apart along swath line trajectories that are far in between. This article describes a new class of satellite remote sensing LiDARs, aimed at overcoming the limitations of current satellite imaging systems. It exploits the principles of compressive sensing and machine learning (ML) to compressively sense Earth from hundreds of kilometers above Earth to then reconstruct the 3-D imagery with resolution and coverage, as if the data were collected from airborne platforms at just hundreds of meters in height. We introduce a novel representation of waveform altimetry profiles, coined hyperheight data cubes (HHDCs), which encompass rich information about the 3-D structure of a scene. Canopy height models (CHMs), digital terrain models (DTMs), and many other features of a scene that are embedded in HHDC are easily extracted with simple statistical quantiles. We introduce ML methods to reconstruct the compressive LiDAR measurements so as to attain high-resolution, dense coverage, and broad field-of-view per swath pass. ML training data are attained from NASA’s G-LiHT imaging missions. Simulations with various types of forests across the US illustrate the power of the new LiDAR imaging systems.
Graph signal processing (GSP) techniques are powerful tools that model complex relationships within large datasets, being now used in a myriad of applications in different areas including data ...science, communication networks, epidemiology, and sociology. Simple graphs can only model pairwise relationships among data which prevents their application in modeling networks with higher-order relationships. For this reason, some efforts have been made to generalize well-known graph signal processing techniques to more complex graphs such as hypergraphs, which allow capturing higher-order relationships among data. In this article, we provide a new hypergraph signal processing framework (t-HGSP) based on a novel tensor-tensor product algebra that has emerged as a powerful tool for preserving the intrinsic structures of tensors. The proposed framework allows the generalization of traditional GSP techniques while keeping the dimensionality characteristic of the complex systems represented by hypergraphs. To this end, the core elements of the t-HGSP framework are introduced, including the shifting operators and the hypergraph signal. The hypergraph Fourier space is also defined, followed by the concept of bandlimited signals and sampling. In our experiments, we demonstrate the benefits of our approach in applications such as clustering and denoising.
Representation learning considering high-order relationships in data has recently shown to be advantageous in many applications. The construction of a meaningful hypergraph plays a crucial role in ...the success of hypergraph-based representation learning methods, which is particularly useful in hypergraph neural networks and hypergraph signal processing. However, a meaningful hypergraph may only be available in specific cases. This paper addresses the challenge of learning the underlying hypergraph topology from the data itself. As in graph signal processing applications, we consider the case in which the data possesses certain regularity or smoothness on the hypergraph. To this end, our method builds on the novel tensor-based hypergraph signal processing framework (t-HGSP) that has recently emerged as a powerful tool for preserving the intrinsic high-order structure of data on hypergraphs. Given the hypergraph spectrum and frequency coefficient definitions within the t-HGSP framework, we propose a method to learn the hypergraph Laplacian from data by minimizing the total variation on the hypergraph (TVL-HGSP). Additionally, we introduce an alternative approach (PDL-HGSP) that improves the connectivity of the learned hypergraph without compromising sparsity and use primal-dual-based algorithms to reduce the computational complexity. Finally, we combine the proposed learning algorithms with novel tensor-based hypergraph convolutional neural networks to propose hypergraph learning-convolutional neural networks (t-HyperGLNN).
This thesis proposes a multimodal imaging system that allows reconstructing a dense 3D spectral point cloud. The system consists of an Intel RealSense D415 depth camera that includes active infrared ...stereo and a NuruGo Smart Ultraviolet (UV) camera. RGB and Near Infrared (NIR) images are obtained from the first camera and UV from the second one. The novelty of this work is in the application of a perpixel calibration method using CALTag (High Precision Fiducial Markers for Camera Calibration) that outperforms traditional camera’s calibration, which is based on a pinhole-camera model and a checker pattern. The new method eliminates both lens distortions and depth distortion with simple calculations on a Graphics Processing Unit (GPU), using a rail calibration system. To this end, the undistorted 3D world coordinates for every single pixel are generated using only six parameters and three linear equations. The traditional pinhole camera model is substituted by two polynomial mapping models. One handles lens distortions and the other one handles the depth distortions. The use of CALTag instead of traditional checkerboards allows overcoming failures during calibration due to clipping or occlusion of the calibration pattern. Multiple point clouds from different points of view of an object are registered using iterative closest point (ICP) algorithm. Finally, a novel sampling technique on a multigraph is proposed and demonstrated experimentally on a 3D spectral point cloud generated by the proposed multimodal imaging system.
Hypergraph Neural networks (HyperGNNs) and hypergraph signal denoising (HyperGSD) are two fundamental topics in higher-order network modeling. Understanding the connection between these two domains ...is particularly useful for designing novel HyperGNNs from a HyperGSD perspective, and vice versa. In particular, the tensor-hypergraph convolutional network (T-HGCN) has emerged as a powerful architecture for preserving higher-order interactions on hypergraphs, and this work shows an equivalence relation between a HyperGSD problem and the T-HGCN. Inspired by this intriguing result, we further design a tensor-hypergraph iterative network (T-HGIN) based on the HyperGSD problem, which takes advantage of a multi-step updating scheme in every single layer. Numerical experiments are conducted to show the promising applications of the proposed T-HGIN approach.
