recursive function on each pixel in google earth engine

Question

I want to filter time series in the google earth engine which requires two for loops over time-series of a single pixel. I searched around and not found any example related to this. I know about .map function and I am using it for the generation of RVI on the earth engine. I found about .toArray function but not found any example related to my problem.

I will appreciate any help in this regard. Also, I am new to the earth engine so this may be a trivial question for others.

This is the code that I have. I took it from a blog and modified it according to my need. I am stuck after this.

var sentinel1 = ee.ImageCollection('COPERNICUS/S1_GRD_FLOAT');

// Filter VH, IW
var vh = sentinel1
  // Filter to get images with VV and VH dual polarization.
  //.filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VH'))
  // Filter to get images collected in interferometric wide swath mode.
  .filter(ee.Filter.eq('instrumentMode', 'IW'))
  // reduce to VH polarization
  //.select('VH')
  // filter 10m resolution
  .filter(ee.Filter.eq('resolution_meters', 10));
// Filter to orbitdirection Descending
var vhDescending = vh.filter(ee.Filter.eq('orbitProperties_pass', 'DESCENDING'));
// Filter time 2015
var vhDesc2015 = vhDescending.filterDate(ee.Date('2021-01-01'), ee.Date('2021-04-30'));

// Filter to MKD roi
var s1_mkd = vhDesc2015.filterBounds(roi);

print('All metadata:', s1_mkd);
var count = s1_mkd.size();
print('Count: ', count);



//var dates = s1_mkd.aggregate_array("system:time_start")
//print('dates: ', dates);

var dates = s1_mkd
    .map(function(image) {
      return ee.Feature(null, {'date': image.date().format('YYYY-MM-dd')})
    })
    .distinct('date')
    .aggregate_array('date')
    
print('dates: ', dates);

var featureCollection = ee.FeatureCollection(dates
                        .map(function(element){
                        return ee.Feature(null,{prop:element})}))


//Export a .csv table of date, mean NDVI for watershed
Export.table.toDrive({
  collection: featureCollection,
  description: 'Timeseries',
  folder: 'WC_raw',
  fileFormat: 'CSV',
});

var rvi4s1 = function(img){
  var vh = img.select('VH');
  var vv = img.select('VV');
  var col = vv.divide(vv.add(vh)).sqrt().rename('dop');
  var dop = col.select('dop')
  var value = dop.multiply(vh.multiply(4).divide(vv.add(vh))).rename('rvi4s1');
  return value;
};

var rvi = s1_mkd.map(rvi4s1);
print(rvi);