How to mask PCA on Google Earth Engine

Question

I am trying to perform PCA on MODIS imagery. I got my code to run using MODIS (it also worked for Landsat), but when I mask my MODIS collection the PCA fails. This had to do with missing values, as GEE doesn't run on sparse matrices.

Question: How do I mask bad pixels during a PCA? One can not mask before the PCA, so how can I mask pixels after PCA?

Here is my code. Extent is my ROI.

var dataset2019 = ee.ImageCollection('MODIS/006/MCD43A4').filter(ee.Filter.date('2018-12-01', '2019-04-20'));
var dataset2020 = ee.ImageCollection('MODIS/006/MCD43A4').filter(ee.Filter.date('2019-12-01', '2020-04-20'));
var modisCol = dataset2019.merge(dataset2020);

// Create a QA mask function
var filterqa = function(image){ 
  var mask1 = image.select("BRDF_Albedo_Band_Mandatory_Quality_Band1").eq(0);
  var mask2 = image.select("BRDF_Albedo_Band_Mandatory_Quality_Band2").eq(0);
  var mask3 = image.select("BRDF_Albedo_Band_Mandatory_Quality_Band3").eq(0);
  var mask4 = image.select("BRDF_Albedo_Band_Mandatory_Quality_Band4").eq(0);
  var mask5 = image.select("BRDF_Albedo_Band_Mandatory_Quality_Band5").eq(0);
  var mask6 = image.select("BRDF_Albedo_Band_Mandatory_Quality_Band6").eq(0);
  var mask7 = image.select("BRDF_Albedo_Band_Mandatory_Quality_Band7").eq(0);
  return image.updateMask(mask1).updateMask(mask2).updateMask(mask3).updateMask(mask4)
  .updateMask(mask5).updateMask(mask6).updateMask(mask7);
};

// Preparing imagery for PCA
var PCA = function(image){
  var image = image.select(['Nadir_Reflectance_Band1','Nadir_Reflectance_Band2', 
        'Nadir_Reflectance_Band3','Nadir_Reflectance_Band4',
        'Nadir_Reflectance_Band5','Nadir_Reflectance_Band6',
        'Nadir_Reflectance_Band7']);
  var orig = image;
  var region = Extent;
  var scale = 500;
  var bandNames = ['Nadir_Reflectance_Band1','Nadir_Reflectance_Band2',
  'Nadir_Reflectance_Band3','Nadir_Reflectance_Band4','Nadir_Reflectance_Band5',
  'Nadir_Reflectance_Band6','Nadir_Reflectance_Band7'];
  var meanDict = image.reduceRegion({
    reducer: ee.Reducer.mean(),
    geometry: region,
    scale: scale,
    maxPixels: 1e9
  });
  var means = ee.Image.constant(meanDict.values(bandNames));
  var centered = image.subtract(means);
  var getNewBandNames = function(prefix) {
  var seq = ee.List.sequence(1, 7);
  return seq.map(function(b) {
    return ee.String(prefix).cat(ee.Number(b).int());
    });
  };
  // PCA function
  var getPrincipalComponents = function(centered, scale, region) {
    var arrays = centered.toArray();
    var covar = arrays.reduceRegion({
      reducer: ee.Reducer.centeredCovariance(),
      geometry: region,
      scale: scale,
      maxPixels: 1e9
    });
    var covarArray = ee.Array(covar.get('array'));
    var eigens = covarArray.eigen();
    var eigenValues = eigens.slice(1, 0, 1);
    var eigenVectors = eigens.slice(1, 1);
    var arrayImage = arrays.toArray(1);
    var principalComponents = ee.Image(eigenVectors).matrixMultiply(arrayImage);
    var sdImage = ee.Image(eigenValues.sqrt())
    .arrayProject([0]).arrayFlatten([getNewBandNames('sd')]);
    return principalComponents.arrayProject([0])
    .arrayFlatten([getNewBandNames('pc')])
    .divide(sdImage);
    };
  var pcImage = getPrincipalComponents(centered, scale, region);
  return ee.Image(image.addBands(pcImage));
};

var modisColClip = modisCol
.map(function(image){return(image.clip(Extent))})
.map(filterqa)
.map(PCA)
.sort('system:time_start');
print("modis",modisColClip);

This code produces a error due to the masking of pixels. How can I change this? I have tried to swap around the order of functions to map, but I don't want to conduct a PCA using QA bands, and if I ignore the QA bands, the filter function fails because there is no QA bands.

Any idea?

Answer 1

One needs to perform a Join to mask pixel after performing PCA. Basically, after performing PCA, you have to Join it with the original imagery that contained the QA bands (modisCol).

// Compile PCA collection
var PCAColClip = modisCol
.map(function(image){return(image.clip(Extent))})
.map(PCA)
.sort('system:time_start')
.select(['pc1']);
print("modis PCA",PCAColClip);

// Mask PCA using original QA bands
var mod1 = modisCol.map(function(image){return(image.clip(Extent))});
var mod2 = PCAColClip;
var filter = ee.Filter.equals({
  leftField: 'system:time_start',
  rightField: 'system:time_start'
});
var simpleJoin = ee.Join.inner();
var innerJoin = ee.ImageCollection(simpleJoin.apply(mod1, mod2, filter));
var joined = innerJoin.map(function(feature) {
  return ee.Image.cat(feature.get('primary'), feature.get('secondary'));
});
// Compile PCA collection
var PCAMasked = joined
.map(filterqa)
.select(['pc1']);
print("modis PCA Masked",PCAMasked);