Fixing Plasma Image Retention
Leaving a static image on the screen for an hour shouldn't cause permanent burn-in, though it could result in temporary image retention. In that case, I would think you'd see ghosting elsewhere in on the screen in addition to the station logo.
Like all Panasonic plasmas, the G15 provides several "anti image retention" features in the Setup menu, including the ability to display gray sidebars on the sides of a 4:3 image and a "pixel orbiter" that shifts the image around by a few pixels every so often. However, neither of these are likely to solve your problem. The one you want is called "Scrolling bar," which scrolls a vertical white bar across an otherwise black screen. After you engage the scrolling bar, you can turn it off by pressing any key on the remote (except Power), or it will disengage automatically if you do nothing for 15 minutes. This should help reduce or eliminate the ghosting you see, though it might take a few runs.
As I was researching this question, I came across a downloadable video that can be burned to recordable DVD. It's called "Plasma TV Logo Removing DVD," and it's available here in either NTSC or PAL format. The program displays randomly changing video noise, such as that shown above, at different resolutions, which you can run for 30 minutes to two hours or more. Since the image is constantly changing, there is no risk of image retention if you display it for long periods of time.
Otherwise, you can get the Digital Video Essentials setup DVD, which has full-screen fields that fill the entire screen with white or gray at a uniform intensity. (Interestingly, the Digital Video Essentials: HD Basics Blu-ray does not have full-screen white and gray fields.) Display the 100-percent white field for a while, and you should start to see the ghost fade. You can leave this image on the screen indefinitely, since it has no distinct elements, so it won't cause image retention.
And while you have the setup disc playing, be sure to select the Standard or THX picture mode and set the basic picture controls (Contrast, Brightness, Color, Tint, and Sharpness) to their optimum settings. This will help reduce the chance of image retention in the future.
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