Recently, there is a resurgence of interest in uncoded transmission for wireless visual communication. While conventional coded systems suffer from cliff effect as the channel condition varies dynamically, uncoded linear-transformed transmission (ULT) provides elegant quality degradation for wide channel SNR range. ULT skips non-linear operations, such as quantization and entropy coding. Instead, it utilizes linear decorrelation transform and linear scaling power allocation to achieve optimized transmission. This paper presents a theoretical analysis for power-distortion optimization of ULT. In addition to the observation in our previous work that a decorrelation transform can bring significant performance gain, this paper reveals that exploiting the energy diversity in transformed signal is the key to achieve the full potential of decorrelation transform. In particular, we investigated the efficiency of ULT with exact or inexact signal statistics, highlighting the impact of signal energy modeling accuracy. Based on that, we further proposed two practical energy modeling schemes for ULT of visual signals. Experimental results show that the proposed schemes improve the quality of reconstructed images by 3~5 dB, while reducing the signal modeling overhead from hundreds or thousands of meta data to only a few meta data. The perceptual quality of reconstruction is significantly improved.