Use a custom loss function
Only compare the model's prediction to the real values at the 15 pixels, and leave the rest.
Keep your CNN simple
Use a few convolution layers (e.g., 2 or 3) with ReLU. Since your problem is small, you don’t need anything to complicate it.
Train it to focus
Make sure the model is trained to only care about the 15 pixels that are "on". Pass the binary mask to guide where it should look.