Soft video delivery, i.e., analog video transmission, has been proposed to provide graceful 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. It causes large overheads and quality degradation because of rate and power losses. To reduce the overheads while keeping high video quality, we propose a new analog transmission scheme. Our scheme exploits a Gaussian Markov random field 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 our proposed scheme reduces overheads by 97 % with 3.4 dB improvement of video quality compared to the existing analog video transmission scheme.