Characterization of Color Images with Multiscale Monogenic Maxima

Clifford Wavelet Entropy for Fetal ECG Extraction

Analysis of the fetal heart rate during pregnancy is essential for monitoring the proper development of the fetus. Current fetal heart monitoring techniques lack the accuracy in fetal heart rate monitoring and features acquisition, resulting in diagnostic medical issues. The challenge lies in the extraction of the fetal ECG from the mother ECG during pregnancy. This approach has the advantage of being a reliable and non-invasive technique. In the present paper, a wavelet/multiwavelet method is proposed to perfectly extract the fetal ECG parameters from the abdominal mother ECG. In a first step, due to the wavelet/mutiwavelet processing, a denoising procedure is applied to separate the noised parts from the denoised ones. The denoised signal is assumed to be a mixture of both the MECG and the FECG. One of the well-known measures of accuracy in information processing is the concept of entropy. In the present work, a wavelet/multiwavelet Shannon-type entropy is constructed and applied to evaluate the order/disorder of the extracted FECG signal. The experimental results apply to a recent class of Clifford wavelets constructed in Arfaoui, et al. J. Math. Imaging Vis. 2020, 62, 73-97, and Arfaoui, et al.Acta Appl. Math.2020, 170, 1-35.. Additionally, classical Haar-Faber-Schauder wavelets are applied for the purpose of comparison. Two main well-known databases have been applied, the DAISY database and the CinC Challenge 2013 database. The achieved accuracy over the test databases resulted in Se=100%, PPV=100% for FECG extraction and peak detection.

Phase estimation of a 2D fringe pattern using a monogenic-based multiscale analysis

In this paper, a multiscale monogenic analysis is applied to 2D interference fringe patterns. The monogenic signal was originally developed as a 2D generalization of the well-known analytic signal in the 1D case. The analytic and monogenic tools are both useful to extract phase information, which can then be directly linked with physical quantities. Previous studies have already shown the interest in the monogenic signal in the field of interferometry. This paper presents theoretical and numerical illustrations of the connection between the physical phase information and the phase estimated with the monogenic tool. More specifically, the ideal case of pure cosine waves is deeply studied, and then the complexity of the fringe patterns is progressively increased. One important weakness of the monogenic transform is its singularity at the null frequency, which makes the phase estimations of low-frequency fringes diverge. Moreover, the monogenic transform is originally designed for narrowband signals, and encounters difficulties when dealing with noised signals. These problems can be bypassed by performing a multiscale analysis based on the monogenic wavelet transform. Moreover, this paper proposes a simple strategy to combine the information extracted at different scales in order to get a better estimation of the phase. The numerical tests (synthetic and real signals) show how this approach provides a finer extraction of the geometrical structure of the fringe patterns.