Would it be possible to reconstruct 3d trajectory of ball projectile using only monocular video
I guess this is what Olli implies: Using a lens distortion matrix if necessary, the center of the ball in the picture gives you an elevation and azimuth of your ball relative to the focal point of your camera. The size of the ball image gives you distance.

That's a point in 3D space.

From there, it's really only a manner of grammar school level math to estimate the four (or only three – do you know the mass of the planet you're on?) unknowns in your problem (three components of initial velocity, and maybe magnitude of gravity), at least without considerations for measurement error from multiple observations of the ball.

If you need to take measurement error (finite shutter speed, finite frame rate, finite camera resolution, imperfect estimation of position from picture) into account, well, feels like the classical problem where you'd throw a Kalman at it and be done.

In fact, I think this nice little article "How a Kalman filter works, in pictures" has an explanation that nearly completely describes a solution for your specific problem.