I am using the ESA open scientific data hub for Sentinel 1 SAR imagery (Interferometric Wide swath SLC VV polarization) and would like to know how to perform vegetation health analysis from this data? What tools are available for this using ESA's SNAP open source software?
No way to calculate NDVI from SAR imagery, like Sentinel-1 images(any polarisations). To calculate NDVI you could get 2 bands (Near Infrared and Red bands) from Sentinel-2 or Landsat-8.
So, about SAR. You just only can get some value about biomass or LAI (Leaf Area Index) and after that you can try to search some formulas to indexing vegetation for specific fields, agricultural, forests or something else.
According to me there are three (or four) possible way so far. 1)Leaf Area index from Statistics or water cloud model. 2) Radar Vegetation Index (RVI) from Dual-pol or quad-pol system and Radar degradation forest index from Dual-pol system. However, all these approaches are not simple and have lots of difficulties and limitations. Please try to read some scientific research about these indices.
This article explains how to compute NDVI from sentinel 1 and also compare the results with NDVI computation from Landsat 8.