Iterating to calculate mean NDVI and mask pixels having greater than mean NDVI value of each image in image collection using Google Earth Engine

Question

I am working on Sentinel -2 image collection over my study region in Google Earth Engine. I can calculate Mean NDVI for an image using ee.Reducer.mean() and mask pixels using update mask .gt(mean value number). Now I want to do this to each image of the collection. Since mean NDVI value of each image will be different I am facing difficulty to use .map function.I attempted this but I think I have got it all wrong and now I am stuck. How can I iterate it to each image in image collection?

    /////////////Sentinel-2 Burned Area Detection/////////////////////////////////////
    ////Get image collection with specified cloud percentage threshold.
    var s2= ee.ImageCollection("COPERNICUS/S2_SR").filter(ee.Filter.lt("CLOUDY_PIXEL_PERCENTAGE", 10));
    var admin2 = ee.FeatureCollection("FAO/GAUL_SIMPLIFIED_500m/2015/level2");
    var Bhopal = admin2.filter(ee.Filter.eq('ADM2_NAME', 'Bhopal'))
    var geometry = Bhopal.geometry()
    ////vis parameters.
    var vis = {bands: ['B4', 'B3', 'B2'], max: 2000, gamma: 1.5};
    ////print fire occurance.
    // print(ee.String('Fire incident occurred between ').cat(fire_start).cat(' and ').cat(fire_end));
    ////Define Study area
    var area = ee.FeatureCollection(geometry);
    var opacity = 0.5; // number [0-1]
    Map.centerObject(area, 6.5);
    ////Filter Dates for rabi season
    /////March
    var fireImColA1 = ee.ImageCollection(s2.filterDate('2019-03-01', '2019-03-07')  //// Filter by dates.
        .filterBounds(area));
    //// Creat a Cloud Mask.
    function maskS2sr(image) {
      var cloudBitMask = ee.Number(2).pow(10).int(); ////cloud band
      var cirrusBitMask = ee.Number(2).pow(11).int();//// cirrus band
      
      var qa = image.select('QA60'); //// Get the pixel QA band.
      
      var mask = qa.bitwiseAnd(cloudBitMask).eq(0)  ////  Flags set to zero for clear conditions.
          .and(qa.bitwiseAnd(cirrusBitMask).eq(0)); ////  Flags set to zero for clear conditions.
      
      return image.updateMask(mask) //// Return the masked image, scaled to TOA reflectance, without the QA bands.
          .copyProperties(image, ["system:time_start"]);
    }
    
    //// Apply cloud mask to pre and post fire image collections
    /////March
    var fire_CM_ImColA1 = fireImColA1.map(maskS2sr);
    ///Function  add NDVI band to image collection
    var addNDVI = function(image) {
      return image.addBands(image.normalizedDifference(['B8', 'B4']).rename('NDVI'));
    };
    /////Add bands//////
    var fire_WM_ImColA1 = fire_CM_ImColA1.map(addNDVI);
    ////meanNDVI///
    var mean_ndvi = function(image){
      var ndvi = image.select(['NDVI']);
    var ndvi_mean = ndvi.reduceRegion({
      reducer: ee.Reducer.mean(),
      geometry: geometry,
      scale: 20,
      maxPixels: 10e18,
    });
    return ndvi_mean;
    };
    
    var fire_ImColA1 = fire_WM_ImColA1.map(mean_ndvi);
    var mean_mask = function(image){
    var mask = image.select(['mean_ndvi']);
      return image.addBands(ee.Image(1).updateMask(mean_mask.gt(mean_mask)).rename('mean_mask'));
  };
print (fire_ImColA1); 

Answer 1

This can be done simply with one function that you map to every image of the collection.

var apply_Mean_Mask = function(image){
    var ndvi = image.select('NDVI');
    var ndvi_mean = ndvi.reduceRegion({
        reducer: ee.Reducer.mean(),
        geometry: geometry,
        scale: 20,
        maxPixels: 10e18,
    }).getNumber("NDVI");
    return image.updateMask(ndvi.gt(ndvi_mean));
};

var maskedImageCollection = fire_WM_ImColA1.map(apply_Mean_Mask);

You were nearly there, just needed to add one step to your mean_ndvi function.