RESUMEN
Electrocardiography is a valuable tool to aid in medical understanding and treatment of heart-related ailments, specifically atrial fibrillation (AF) and other irregular cardiac behavior. Although signs of AF will manifest in conventional electrocardiogram (ECG) recordings, interpretation and localization of AF sources require significant clinical expertise. In this vein, electrocardiographic imaging has emerged as an important medical imaging modality that provides reconstructions of the heart's electrical activity from non-invasive multi-lead body-surface ECG and anatomical x-ray computed tomography images. In this paper, we present a nonlinear inversion model for computing this mapping to improve upon the reconstruction performance of current methods. While contemporary techniques typically determine an inverse solution by discretizing and inverting an underdetermined linear system of partial differential equations governing the relationship between voltage potentials of the heart and torso, the presented technique re-casts this problem as a task in function approximation and provides a direct parameterization of the inverse operator using a polynomial neural network. That is, the outlined nonlinear inversion technique is a generalization of contemporary reconstruction techniques which allows geometrical and material parameterizations of the forward-model to be optimized using real experimental data collected from patients suffering from AF, as to better represent the inverse operator with respect to reconstruction metrics applicable to electrophysiology. The accuracy of our model is evaluated against a dataset of real-patient recordings to demonstrate its validity, and mathematical analysis is provided to support the polynomial expansion used in our inversion model.
RESUMEN
Information-theoretic analyses for data hiding prescribe embedding the hidden data in the choice of quantizer for the host data. In this paper, we propose practical realizations of this prescription for data hiding in images, with a view to hiding large volumes of data with low perceptual degradation. The hidden data can be recovered reliably under attacks, such as compression and limited amounts of image tampering and image resizing. The three main findings are as follows. 1) In order to limit perceivable distortion while hiding large amounts of data, hiding schemes must use image-adaptive criteria in addition to statistical criteria based on information theory. 2) The use of local criteria to choose where to hide data can potentially cause desynchronization of the encoder and decoder. This synchronization problem is solved by the use of powerful, but simple-to-implement, erasures and errors correcting codes, which also provide robustness against a variety of attacks. 3) For simplicity, scalar quantization-based hiding is employed, even though information-theoretic guidelines prescribe vector quantization-based methods. However, an information-theoretic analysis for an idealized model is provided to show that scalar quantization-based hiding incurs approximately only a 2-dB penalty in terms of resilience to attack.