The first step to achieving what you are asking for would be to find the normalized texture coordinates a.k.a UV-coordinates of the pixel. This can be done as described by AJ Weeks in his answer. However, I wouldn't divide by
height-1, but instead, I would add
0.5 to the x- and y-coordinate and divide by the full width and height. This should give you the "center" of each pixel. As an example, say you have an 8x8 texture and index 10. This would yield
y=2. After the addition, you get
y=2.5. Dividing each of those by 8 gives you the normalized texture coordinates of
Depending on how you render your image, the next step might be a little bit tricky. In general, if your texture is mapped onto an arbitrary mesh, you need to find the triangle that includes the UV-coordinates of the pixel by performing a 2d-point-in-triangle test against the triangles' vertices UV-coordinates. Notice, that depending on your mesh's texture coordinates, there might be more than one triangle or none if you use the texture repetitively or only a certain area of it. If this is not the case, there still might be multiple triangles that contain it, if the point lies on a boundary or vertex. In this case, pick an arbitrary triangle, since the result should be the same.
Now if you have found the triangle determine the barycentric coordinates of the pixel from its UV-coordinates and the vertices of the triangle. Then use those coordinates and multiply them with the vertices 3d coordinates to get the actual 3d coordinates of the pixel in model space.
Finally, perform the usual transformations with your transformation matrices -> model to world -> world to camera -> perspective projection. Then you have your NDC coordinates of the pixel.
The determination of the 3d coordinates in model space can be simplified if your model is just a flat rectangular surface described by 4 vertices that has the one and only purpose to display the whole undistorted texture without repetitions, offsets or scaling (means the corner point vertices UV coordinates are either 0 or 1). Then you can perform a linear interpolation of the 3d coordinates in x and y direction where the UV-coordinate values of the pixel are the interpolation weights in the corresponding direction.
It gets even easier if you render your texture as a full-screen image. Then you only need to subtract 0.5 from your UV-coordinates and multiply the result by 2. This transforms the UV-range [0,1] to the NDC range [-1,1]. The depth value can be chosen arbitrarily.