To export a black and white color layer with blend mode "Screen".

bw2transparent.pde

PImage img = loadImage("noise_bw.png");
PImage out = createImage(img.width, img.height, ARGB);
img.loadPixels();
out.loadPixels();
for(int i=0; i<img.width; i++) {
  for(int j=0; j<img.height; j++) {
    color c = img.pixels[j+i*img.width];
    float a = brightness(c);
    out.pixels[j+i*img.width] = color(255, 255, 255, a);
  }
}
out.updatePixels();
out.save("noise.png");