Design of graph filters and filterbanks

International audienceBasic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them or by changing their domain of representation, in order to better extract or analyze the important information they contain. The aim of this chapter is to review general concepts underlying such filters and representations of graph signals. We first recall the different Graph Fourier Transforms that have been developed in the literature, and show how to introduce a notion of frequency analysis for graph signals by looking at their variations. Then, we move to the introduction of graph filters, that are defined like the classical equivalent for 1D signals or 2D images, as linear systems which operate on each frequency of a signal. Some examples of filters and of their implementations are given. Finally, as alternate representations of graph signals, we focus on multiscale transforms that are defined from filters. Continuous multiscale transforms such as spectral wavelets on graphs are reviewed, as well as the versatileapproaches of filterbanks on graphs. Several variants of graph filterbanks are discussed, for structured as well as arbitrary graphs, with a focus on the central point of the choice of the decimation or aggregation operators

Progesterone rise on the day of HCG administration (premature luteinization) in IVF: An overdue update

Premature luteinization (PL) refers to a rise in serum progesterone (P) levels on the day of hCG administration. Most studies used an absolute P level on the day of hCG administration as an indicator of PL, and the cutoff level differed from 0.8 to 2 ng/mL. Some authors defined PL as a P/E2 ratio of >1. There is a marked variation in the incidence (13% to 71%), of PL due to discrepancies in definition, population characteristics and/or treatment protocols. The pathogenesis of PL in COH is still poorly understood. Several hypotheses may be considered to explain this phenomenon: elevation of follicular LH levels, serum accumulation of HCG from HMG, increased LH receptor sensitivity of the granulosa cells to FSH, or poor ovarian response with increased LH sensitivity. The consequences of this premature elevation of serum P on IVF outcome remain controversial. Attempts to prevent COH include: use of Low-dose hCG alone in the late COH stages, flexible antagonist protocol, use of mifepristone, aspiration of a single leading follicle, hCG administration when the levels of serum P exceeded 1.0 ng/mL