Phase-unwrapping method based on local polynomial models and a maximum a posteriori model correction.

Recently, a theory on local polynomial approximations for phase-unwrapping algorithms, considering a state space analysis, has been proposed in Appl. Opt.56, 29 (2017)APOPAI0003-693510.1364/AO.56.000029. Although this work is a suitable methodology to deal with relatively low signal to noise ratios observed in the wrapped phase, the methodology has been developed only for local-polynomial phase models of order 1. The resultant proposal is an interesting Kalman filter approach for estimating the coefficient or state vectors of these local plane models. Thus, motivated by this approach and simple Bayesian theory, and considering our previous research on local polynomial models up to the third order [Appl. Opt.58, 436 (2019)APOPAI0003-693510.1364/AO.58.000436], we propose an equivalent methodology based on a simple maximum a posteriori estimation, but considering a different state space: difference vectors of coefficients for the current high-order polynomial models. Specific estimations of the covariance matrices for difference vectors, as well as noise covariance matrices involved with the correct estimation of coefficient vectors, are proposed and reconstructions with synthetic and real data are provided.

Detection of Depression-Related Tweets in Mexico Using Crosslingual Schemes and Knowledge Distillation.

Mental health problems are one of the various ills that afflict the world's population. Early diagnosis and medical care are public health problems addressed from various perspectives. Among the mental illnesses that most afflict the population is depression; its early diagnosis is vitally important, as it can trigger more severe illnesses, such as suicidal ideation. Due to the lack of homogeneity in current diagnostic tools, the community has focused on using AI tools for opportune diagnosis. Unfortunately, there is a lack of data that allows the use of IA tools for the Spanish language. Our work has a cross-lingual scheme to address this issue, allowing us to identify Spanish and English texts. The experiments demonstrated the methodology's effectiveness with an F1-score of 0.95. With this methodology, we propose a method to solve a classification problem for depression tweets (or short texts) by reusing English language databases with insufficient data to generate a classification model, such as in the Spanish language. We also validated the information obtained with public data to analyze the behavior of depression in Mexico during the COVID-19 pandemic. Our results show that the use of these methodologies can serve as support, not only in the diagnosis of depression, but also in the construction of different language databases that allow the creation of more efficient diagnostic tools.