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Eliminate scaling from perspective transform

I would like to project an image to a textured wall. Using various techniques I was able to detect the wall plane, and now I just want to draw the image on that plane.

The plane itself is a quadrangle, and I was able to get a perspective transform matrix between the image and the wall plane, and use that transform to perform the projection. My only problem is that the image is scaled up to occupy the entire quadrangle of the wall plane. I would only like it to follow its perspective, without the changes in scale. Can I somehow eliminate the scaling from the transformation matrix, or is there any other method that would help?

Thank you!