A filtering algorithm is proposed for processing images generated by TV holography that contain phase jumps and a high noise level. This algorithm first performs phase unwrapping without removing the noise. After that, it removes the noise by use of a conventional low-pass filter. The new approach allows for using low-pass filters with narrow passbands, leading to a better signal-to-noise ratio in the desired signal. Simulation results are presented and discussed. The new algorithm has been applied successfully under real conditions in a holographic station.