Browsing by Author "Lau, Daniel L."
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Item Block-based spectral image reconstruction for compressive spectral imaging using smoothness on graphs(Optics Express, 2022-02-17) Florez-Ospina, Juan F.; Alrushud, Abdullah K. M.; Lau, Daniel L.; Arce, Gonzalo R.A novel reconstruction method for compressive spectral imaging is designed by assuming that the spectral image of interest is sufficiently smooth on a collection of graphs. Since the graphs are not known in advance, we propose to infer them from a panchromatic image using a state-of-the-art graph learning method. Our approach leads to solutions with closed-form that can be found efficiently by solving multiple sparse systems of linear equations in parallel. Extensive simulations and an experimental demonstration show the merits of our method in comparison with traditional methods based on sparsity and total variation and more recent methods based on low-rank minimization and deep-based plug-and-play priors. Our approach may be instrumental in designing efficient methods based on deep neural networks and covariance estimation.Item QRnet: fast learning-based QR code image embedding(Multimedia Tools and Applications, 2022-02-16) Pena-Pena, Karelia; Lau, Daniel L.; Arce, Andrew J.; Arce, Gonzalo R.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.Item t-HGSP: Hypergraph Signal Processing Using t-Product Tensor Decompositions(IEEE Transactions on Signal and Information Processing over Networks, 2023-05-16) Pena-Pena, Karelia; Lau, Daniel L.; Arce, Gonzalo R.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.