Examinando por Materia "Transformada de Fourier"
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Publicación Análisis de técnicas Wavelet para el desarrollo de compresores de audio(Universidad EAFIT, 2017) Medina Sánchez, Laura Victoria; Villegas Gutiérrez, Jairo AlbertoPublicación Compresión de imágenes usando wavelets(Universidad EAFIT, 2007) Puetamán Guerrero, Gloria; Salazar Escobar, Hernán; Villegas Gutiérrez, Jairo AlbertoPublicación Método basado en aprendizaje profundo para la mitigación de artefactos espejo y el Aliasing producido por el submuestreo lateral en el dominio de Fourier en la tomografía de coherencia óptica(Universidad EAFIT, 2025) Pulgarín Suárez, Diego Alexander; Restrepo Gómez, René; Trujillo Anaya, Carlos Alejandro; Cadavid Muñoz, Juan JoséOptical Coherence Tomography (OCT) is an imaging technique that has revolutionized medical diagnosis by providing high-resolution, three-dimensional images of biological tissues non-invasively. Its initial implementation, Time-Domain OCT (TD-OCT), relied on mechanical scanning to acquire each depth profile, which limited its speed and made it susceptible to motion artifacts from the patient, compromising the quality of in-vivo images. To overcome these limitations, Fourier-Domain OCT (FD-OCT) was developed, which captures the entire information of a depth profile simultaneously. This advancement dramatically increased speed and sensitivity but also introduced new challenges. One of the most significant is the mirror artifact, a conjugate copy of the image that appears due to the real nature of the interferometric signal and its subsequent Fourier Transform. Another key problem is aliasing, which arises from the trade-off between acquisition speed and compliance with the Nyquist sampling theorem. In practice, lateral sampling density is reduced to minimize scan time and motion artifacts, but this undersampling causes high spatial frequencies of the tissue to be incorrectly represented as lower frequencies, degrading image fidelity. The primary goal of the research is to address two specific problems: lateral undersampling, which causes aliasing, and the mirror artifact. Solving the former would allow for reduced acquisition time without sacrificing tomogram quality, while eliminating the latter would optimize the use of the image's depth range. Traditionally, solutions for these artifacts have depended on hardware modifications to the OCT system. These approaches, while effective, are costly, increase equipment complexity, and are not easily applicable to existing systems in clinical settings. In response to these limitations, this work proposes an innovative solution based on deep learning that operates exclusively in the digital post-processing stage of the images. The main advantage of this method is that it requires no physical intervention in the optical system, allowing it to be implemented on data acquired with any conventional OCT equipment. To carry out this task, different Generative Adversarial Network (GAN) architectures were explored, with the Pix2Pix model being identified as the most effective for simultaneously correcting both aliasing artifacts from undersampling and the mirror artifact. The effectiveness of this methodology was rigorously validated through qualitative and quantitative analyses. This research not only demonstrates the potential of GANs to solve complex problems in OCT imaging but also lays a solid foundation for their future application in clinical practice. By improving image quality and acquisition efficiency without the need for new hardware, this post-processing approach has the potential to significantly optimize diagnosis, where accuracy and speed are essential.Publicación Método Wavelet-Petrov-Galerkin en la solución numérica de la ecuación KdV(Universidad EAFIT, 2011) Duarte Vidal, Julio César; Fierro Yaguara, Esper Andrés; Villegas Gutiérrez, Jairo Alberto; Castaño Bedoya, Jorge Iván