save() uses the ImageIO.write() Java call to do the save.
It uses an arbitrary image writer (chosen internally by Java), depending on file extension, to do the job. With a default, medium quality.
There is a page explaining how to do the save yourself with chosen quality: Adjust JPEG image compression quality when saving images in Java.
In Processing, the core of save() is:
Code:

    try {
	BufferedImage bimage =
	  new BufferedImage(width, height, (format == ARGB) ?
				  BufferedImage.TYPE_INT_ARGB :
				  BufferedImage.TYPE_INT_RGB);
	bimage.setRGB(0, 0, width, height, pixels, 0, width);
	File file = new File(path);
	String extension = path.substring(path.lastIndexOf('.') + 1);

	ImageIO.write(bimage, extension, file);
    } catch (Exception e) {
	e.printStackTrace();
	throw new IOException("image save failed.");
    }
  } 

so you can do your own save() based on this code, using the given improvement.