Image math (reduction) within image collection

Question

I want to generate monthly average Sentinel-1 images in GEE and adapted this answer here to get 12 mean radar images over a year. However, as radar imagery in GEE is in decibel, this returns the geometric mean and not the arithmetic mean. I have been able to convert a single decibel image to power using the equation:

var PWR = ee.Image(10).pow(image.select('VH').divide(10))

but I do not know how to implement this over each image in a collection prior to calculating the monthly average. Is it possible to calculate this when generating an image collection?

My code is:

var sentinel1 = ee.ImageCollection("COPERNICUS/S1_GRD");

var months = ee.List.sequence(1, 12);

var byMonth = ee.ImageCollection.fromImages(
    months.map(function (m) {
      return sentinel1
      .filter(ee.Filter.eq('instrumentMode', 'IW'))
      .filterBounds(geometry)
      .filterDate('2017-01-01','2017-12-31')
      .filter(ee.Filter.calendarRange(m, m, 'month'))
                .select('VH')
                .mean()
                .set('month', m);
}));

and a working example can be found here

Answer 1

You would need to map a function over the entire Sentinel-1 collection to apply the power calculation to each image. Here is an example:

var geometry = ee.Geometry.Point([-122,37.5])

// apply all of the filtering up front to prevent processing on large image collection
var sentinel1 = ee.ImageCollection("COPERNICUS/S1_GRD")
  .filter(ee.Filter.eq('instrumentMode', 'IW'))
  .filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VH'))
  .filterBounds(geometry)
  .filterDate('2017-01-01','2017-12-31');

// converting decibels to power for the VH polarization
var power = sentinel1.map(function(image){
  return ee.Image(10).pow(image.select('VH').divide(10))
    .rename('VH') // rename band
    .copyProperties(image,['system:time_start']); // copy time property for later
});

// months to map over
var months = ee.List.sequence(1,12);

var byMonth = ee.ImageCollection.fromImages(
  months.map(function (m) {
    return power // using the calculated power images instead of decibel
      .filter(ee.Filter.calendarRange(m, m, 'month')) // get the month of interest
        .select('VH')
        .mean() // mean composite
        .set('month', m);
}));
print(byMonth);

Map.addLayer(ee.Image(byMonth.first()),{min:0,max:1,gamma:4},'Jan. composite');

Here is the link to the code: https://code.earthengine.google.com/d41474f8d717b1c1a67c5a1dea6e8d5e