Soft video delivery, i.e., analog video transmission, has been proposed to provide high video quality in unstable wireless channels. However, existing analog schemes need to transmit a significant amount of metadata to a receiver for power allocation and decoding operations causing large overhead and quality degradation due to rate and power losses. To reduce the overhead while keeping the video quality high, we propose a new analog transmission scheme. Our scheme exploits a Gaussian Markov random field (GMRF) for modeling video sequences to significantly reduce the required amount of metadata, which are obtained by fitting into the Lorentzian function. Our scheme achieves not only reduced overhead but also improved video quality, by using the fitting function and parameters for metadata. Evaluations using several test video sequences demonstrate that the proposed scheme reduces overhead by 99.7 % with 1.2 dB improvement of video quality (in terms of peak signal-to-noise ratio) compared to the existing analog video transmission scheme. We also investigate the impact of bandwidth limitation, showing a significant gain up to 2.7 dB for narrow-band systems.