SENTINEL-1 SPECKLE FILTER: gamma map

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//  Algorithm adapted from https://groups.google.com/g/google-earth-engine-developers/c/a9W0Nlrhoq0/m/tnGMC45jAgAJ.

// Import Sentinel-1 Collection 
var s1 =  ee.ImageCollection('COPERNICUS/S1_GRD')
			.filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VH'))
			.filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VV'))
			.filter(ee.Filter.eq('orbitProperties_pass', 'DESCENDING'))
			.filter(ee.Filter.eq('instrumentMode', 'IW'))
			.filterBounds(geometry)
			.filterDate("2020-10-01","2020-10-31");
			
var firstNoTerrainCorrection = ee.Image(s1.first());

Map.addLayer(firstNoTerrainCorrection,{min:-25,max:20},"no terrain correction");

s1 = s1.map(terrainCorrection);
var s1_gammaMap = s1.map(gammaMap);

var firstTerrainCorrection = ee.Image(s1.first());
var s1_gammaMap  = ee.Image(s1_gammaMap.first());


Map.addLayer(firstTerrainCorrection,{min:-25,max:20},"Terrain corrected");
Map.addLayer(s1_gammaMap,{min:-25,max:20},"Gamma Map");


// Implementation by Andreas Vollrath (ESA), inspired by Johannes Reiche (Wageningen)
function terrainCorrection(image) { 
  var imgGeom = image.geometry();
  var srtm = ee.Image('USGS/SRTMGL1_003').clip(imgGeom); // 30m srtm 
  var sigma0Pow = ee.Image.constant(10).pow(image.divide(10.0));

  // Article ( numbers relate to chapters) 
  // 2.1.1 Radar geometry 
  var theta_i = image.select('angle');
  var phi_i = ee.Terrain.aspect(theta_i)
    .reduceRegion(ee.Reducer.mean(), theta_i.get('system:footprint'), 1000)
    .get('aspect');

  // 2.1.2 Terrain geometry
  var alpha_s = ee.Terrain.slope(srtm).select('slope');
  var phi_s = ee.Terrain.aspect(srtm).select('aspect');

  // 2.1.3 Model geometry
  // reduce to 3 angle
  var phi_r = ee.Image.constant(phi_i).subtract(phi_s);

  // convert all to radians
  var phi_rRad = phi_r.multiply(Math.PI / 180);
  var alpha_sRad = alpha_s.multiply(Math.PI / 180);
  var theta_iRad = theta_i.multiply(Math.PI / 180);
  var ninetyRad = ee.Image.constant(90).multiply(Math.PI / 180);

  // slope steepness in range (eq. 2)
  var alpha_r = (alpha_sRad.tan().multiply(phi_rRad.cos())).atan();

  // slope steepness in azimuth (eq 3)
  var alpha_az = (alpha_sRad.tan().multiply(phi_rRad.sin())).atan();

  // local incidence angle (eq. 4)
  var theta_lia = (alpha_az.cos().multiply((theta_iRad.subtract(alpha_r)).cos())).acos();
  var theta_liaDeg = theta_lia.multiply(180 / Math.PI);
  // 2.2 
  // Gamma_nought_flat
  var gamma0 = sigma0Pow.divide(theta_iRad.cos());
  var gamma0dB = ee.Image.constant(10).multiply(gamma0.log10());
  var ratio_1 = gamma0dB.select('VV').subtract(gamma0dB.select('VH'));

  // Volumetric Model
  var nominator = (ninetyRad.subtract(theta_iRad).add(alpha_r)).tan();
  var denominator = (ninetyRad.subtract(theta_iRad)).tan();
  var volModel = (nominator.divide(denominator)).abs();

  // apply model
  var gamma0_Volume = gamma0.divide(volModel);
  var gamma0_VolumeDB = ee.Image.constant(10).multiply(gamma0_Volume.log10());

  // we add a layover/shadow maskto the original implmentation
  // layover, where slope > radar viewing angle 
  var alpha_rDeg = alpha_r.multiply(180 / Math.PI);
  var layover = alpha_rDeg.lt(theta_i);

  // shadow where LIA > 90
  var shadow = theta_liaDeg.lt(85);

  // calculate the ratio for RGB vis
  var ratio = gamma0_VolumeDB.select('VV').subtract(gamma0_VolumeDB.select('VH'));

  var output = gamma0_VolumeDB.addBands(ratio).addBands(alpha_r).addBands(phi_s).addBands(theta_iRad)
    .addBands(layover).addBands(shadow).addBands(gamma0dB).addBands(ratio_1);

  return image.addBands(
    output.select(['VV', 'VH'], ['VV', 'VH']),
    null,
    true
  );
}


function powerToDb(img){
  return ee.Image(10).multiply(img.log10());
}

function dbToPower(img){
  return ee.Image(10).pow(img.divide(10));
}

function gammaMap(img){

  var ksize = 7;
  var enl = 5;
  var bandNames = img.bandNames();
  
  // Convert image from dB to natural values
  var nat_img = dbToPower(img);

  // Square kernel, ksize should be odd (typically 3, 5 or 7)
  var weights = ee.List.repeat(ee.List.repeat(1,ksize),ksize);
  
  // ~~(ksize/2) does integer division in JavaScript
  var kernel = ee.Kernel.fixed(ksize,ksize, weights, ~~(ksize/2), ~~(ksize/2), false);

  // Get mean and variance
  var mean = nat_img.reduceNeighborhood(ee.Reducer.mean(), kernel);
  var variance = nat_img.reduceNeighborhood(ee.Reducer.variance(), kernel);

  // "Pure speckle" threshold
  var ci = variance.sqrt().divide(mean);  // square root of inverse of enl

  // If ci <= cu, the kernel lies in a "pure speckle" area -> return simple mean
  var cu = 1.0/Math.sqrt(enl);
  
  // If cu < ci < cmax the kernel lies in the low textured speckle area -> return the filtered value
  var cmax = Math.sqrt(2.0) * cu

  var alpha = ee.Image(1.0 + cu*cu).divide(ci.multiply(ci).subtract(cu*cu));
  var b = alpha.subtract(enl + 1.0)
  var d = mean.multiply(mean).multiply(b).multiply(b).add(alpha.multiply(mean).multiply(nat_img).multiply(4.0*enl));
  var f = b.multiply(mean).add(d.sqrt()).divide(alpha.multiply(2.0));
  
  var caster = ee.Dictionary.fromLists(bandNames,ee.List.repeat('float',3));
  var img1 = powerToDb(mean.updateMask(ci.lte(cu))).rename(bandNames).cast(caster);
  var img2 = powerToDb(f.updateMask(ci.gt(cu)).updateMask(ci.lt(cmax))).rename(bandNames).cast(caster);
  var img3 = img.updateMask(ci.gte(cmax)).rename(bandNames).cast(caster);
  
  // If ci > cmax do not filter at all (i.e. we don't do anything, other then masking)
  var result = ee.ImageCollection([img1,img2,img3])
    .reduce(ee.Reducer.firstNonNull()).rename(bandNames);
  
  // Compose a 3 band image with the mean filtered "pure speckle", the "low textured" filtered and the unfiltered portions
  return result;
}