color - how to compensate 50% opacity white over photograph

I have a photo and a while ago I had added a layer on top of it which was pure white at 50% opacity.

How can I compensate that effect to get back the original picture?

I have tried adding a black 50% layer, but the picture becomes too dark and there is not enough contrast.

Answer

You can use a levels adjustment layer. I did this in Photoshop but the same technique can be used in other programs.

On the left I applied a 50% opacity white layer to show the effect. On the right I had the 50% effected text layer and then applied a levels adjustment layer.

Note: I moved the white part of the levels slider so the white background would not darken. This makes every pixel to the right of the white slider completely white.

Result