White Noise Functional Solutions for Wick-Type Stochastic Fractional Mixed KdV-mKdV Equation Using Extended G ′ / G -Expansion Method

In this paper, white noise functional solutions of Wick-type stochastic fractional mixed KdV-mKdV equations have been obtained by using the extended G ′ / G -expansion method and the Hermite transform. Firstly, the Hermite transform is used to transform Wick-type stochastic fractional mixed KdV-mKdV equations into deterministic fractional mixed KdV-mKdV equations. Secondly, the exact traveling wave solutions of deterministic fractional mixed KdV-mKdV equations are constructed by applying the extended G ′ / G -expansion method. Finally, a series of white noise functional solutions are obtained by the inverse Hermite transform.

3D Hermite Transform Optical Flow Estimation in Left Ventricle CT Sequences

Heart diseases are the most important causes of death in the world and over the years, the study of cardiac movement has been carried out mainly in two dimensions, however, it is important to consider that the deformations due to the movement of the heart occur in a three-dimensional space. The 3 D + t analysis allows to describe most of the motions of the heart, for example, the twisting motion that takes place on every beat cycle that allows us identifying abnormalities of the heart walls. Therefore, it is necessary to develop algorithms that help specialists understand the cardiac movement. In this work, we developed a new approach to determine the cardiac movement in three dimensions using a differential optical flow approach in which we use the steered Hermite transform (SHT) which allows us to decompose cardiac volumes taking advantage of it as a model of the human vision system (HVS). Our proposal was tested in complete cardiac computed tomography (CT) volumes ( 3 D + t ), as well as its respective left ventricular segmentation. The robustness to noise was tested with good results. The evaluation of the results was carried out through errors in forwarding reconstruction, from the volume at time t to time t + 1 using the optical flow obtained (interpolation errors). The parameters were tuned extensively. In the case of the 2D algorithm, the interpolation errors and normalized interpolation errors are very close and below the values reported in ground truth flows. In the case of the 3D algorithm, the results were compared with another similar method in 3D and the interpolation errors remained below 0.1. These results of interpolation errors for complete cardiac volumes and the left ventricle are shown graphically for clarity. Finally, a series of graphs are observed where the characteristic of contraction and dilation of the left ventricle is evident through the representation of the 3D optical flow.

A Contactless Respiratory Rate Estimation Method Using a Hermite Magnification Technique and Convolutional Neural Networks

The monitoring of respiratory rate is a relevant factor in medical applications and day-to-day activities. Contact sensors have been used mostly as a direct solution and they have shown their effectiveness, but with some disadvantages for example in vulnerable skins such as burns patients. For this reason, contactless monitoring systems are gaining increasing attention for respiratory detection. In this paper, we present a new non-contact strategy to estimate respiratory rate based on Eulerian motion video magnification technique using Hermite transform and a system based on a Convolutional Neural Network (CNN). The system tracks chest movements of the subject using two strategies: using a manually selected ROI and without the selection of a ROI in the image frame. The system is based on the classifications of the frames as an inhalation or exhalation using CNN. Our proposal has been tested on 10 healthy subjects in different positions. To compare performance of methods to detect respiratory rate the mean average error and a Bland and Altman analysis is used to investigate the agreement of the methods. The mean average error for the automatic strategy is 3.28 ± 3.33 % with and agreement with respect of the reference of ≈98%.