Convert RGBA565 & RGBA566 image to PNG

Question

How do I speed this up? Image1 is composed out of binary RGB565 colours (in little endian) and Image2 is composed out of RGB556 colours (in little endian). And put in the input/ folder where the script is located. I can already do the first image but what about the second?
Do I need to use a different image library (preferably in C)?

from os import makedirs
from os.path import join as osjoin, dirname
from PIL import Image
def uncompressed2(filename, width, height):
    # BGR565
    byte = open(osjoin(application_path, "input", filename + ".PTX"), "rb").read()
    Image.frombuffer("RGB", (width, height), byte, "raw", "BGR;16", 0, 1).save(osjoin(application_path, "output2", filename) + ".PNG")
    print("wrote " + filename)

def uncompressed3Manual(filename, width, height):
    # BGR655
    byte = open(osjoin(application_path, "input", filename + ".PTX"), "rb").read()
    img = Image.new('RGB', (width, height))
    index = 0
    for y in range(0, height):
        for x in range(0, width):
            a = byte[index]
            b = byte[index + 1]
            img.putpixel((x,y), (b & 248, 36 * (b & 7) + (a & 192) // 8, 4 * (a & 63)))
            index += 2
    img.save(osjoin(application_path, "output3", filename) + ".PNG")
    print("wrote " + filename)

# Make dirs
makedirs(osjoin(application_path, "output2"), exist_ok = True)
makedirs(osjoin(application_path, "output3"), exist_ok = True)

# uncompressed2("AQUARIUM1", 568, 320)
# RGB556 image
uncompressed3Manual("BACKGROUND1UNSODDED", 1580, 640)

Image 1: Image 2: This is what I get if I try BGR;16 for the second image:

Answer 1

Heading towards swatting-flies-with-anti-aircraft-gun territory, but you could probably read the data into a numpy array, do the arithmetic with numpy, and build the image from that (if I remember correctly, PIL can take numpy arrays as input). At least that might move the loops inside numpy...